import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from scipy.ndimage import gaussian_filter1d
import seaborn as sns
import matplotlib as mpl
from matplotlib.lines import Line2D
import yaml
from scipy import stats

import sys
sys.path.append('../utils/')
from ImagingUtilities import *

import warnings
warnings.filterwarnings('ignore')

from scipy.optimize import curve_fit
from sklearn.preprocessing import StandardScaler

from sklearn.metrics import mean_squared_log_error, r2_score

with open("../data/resources/rcParams.yaml") as f:
    rcParamsDict = yaml.full_load(f)
    for k in rcParamsDict["rcParams"]:
        print("{} {}".format(k,rcParamsDict["rcParams"][k]))
        plt.rcParams[k] = rcParamsDict["rcParams"][k]
    for k1 in set(list(rcParamsDict)).difference(set(["rcParams"])):
        print("{} {}".format(k1,rcParamsDict[k1]))

figure.dpi 80
savefig.dpi 500
figure.figsize [10, 10]
axes.facecolor None
figure.facecolor None
dotSize 20

line_palette = {
 'CTL01A': '#DBB807',
    'CTL08A': '#0FB248',
    'CTL04E': '#FF0054',
    'CTL02A': '#7B00FF',
'H9': '#72190E',
 'H1': '#994F88',
 'CTL05A': '#1965B0',
 'CTL07C': '#437DBF',
 'CTL06F': '#CAE0AB',
 'CTL09A': '#FFFF00',
 'KTD8.2': '#E65518',
 'UCSFi001-A': '#7BAFDE'}

Load data

total_df = pd.read_csv('../../iPSC_imaging/quantifications/quantification.csv', index_col=0)
add_tp = pd.read_csv('../../iPSC_imaging/quantifications/quantification_addTP.csv', index_col=0)
total_df[ ~ total_df.duplicated()]
total_df = pd.concat([total_df, add_tp])

donor_map_names = {i:j for i, j in zip(total_df['line'], total_df['line'])}
donor_map_names['CHD2WT'] = 'UCSFi001-A'
donor_map_names['CHD8WT'] = 'H9'
total_df['line'] = total_df['line'].map(donor_map_names)
total_df.shape

(2776, 16)

total_df['pixel_size'] = 1.38

total_df['Area (microm2)'] = total_df.total_area * (1.38**2)
total_df['Area (mm2)'] = total_df['Area (microm2)'] * ((1.38 / 1000)**2)

total_df['line'].unique()

array(['H1', 'CTL04E', 'CTL02A', 'CTL05A', 'H9', 'KTD8.2', 'CTL09A',
       'CTL06F', 'CTL08A', 'CTL07C', 'UCSFi001-A', 'CTL01A'], dtype=object)

all_tp = total_df.time_point.unique()
all_tp.sort()
all_tp

array(['01_11_23_t18', '02_11_23_t18', '02_11_23_t9', '03_11_23_t18',
       '03_11_23_t9', '04_11_23_t10', '04_11_23_t18', '05_11_23_t18',
       '05_11_23_t9', '06_11_23_t18', '06_11_23_t9', '07_11_23_t18',
       '07_11_23_t9', '08_11_23_t18', '08_11_23_t9', '09_11_23_t20',
       '09_11_23_t9', '10_11_23_t18', '10_11_23_t9', '11_11_23_t18',
       '11_11_23_t9', '12_11_23_t13', '12_11_23_t18', '13_11_23_t18',
       '13_11_23_t9', '14_11_23_t17', '14_11_23_t9', '15_11_23_t17',
       '15_11_23_t9', '16_11_23_t10', '16_11_23_t18', '17_11_23_t17',
       '17_11_23_t9', '18_11_23_t10', '18_11_23_t18', '19_11_23_t10',
       '19_11_23_t18', '20_11_23_t18', '20_11_23_t9', '21_11_23_t17',
       '21_11_23_t9', '22_11_23_t10', '31_10_23_t18', '31_10_23_t9'],
      dtype=object)

Here I'm adding a few quantifications:

1. norm_factor: the normalization factor, corresponding to the mean area of the area percentage of all lines for each time point post split (called split_time)
2. perc_area_norm: the normalized percentage area, corresponding to the percentage area divided by the the normalization factor (1.)
3. mean_area_tp: the mean area of each line at each time point post split (called split_time)
4. area_error: the percentage "error" of the total area computed with respect to the mean of that line at that time point
5. std: the standard deviation of each area with respect to (3.)
6. cv: the coefficient of variation, corresponding to the ratio between the standard deviation and the mean

total_df['line_split'] = total_df['line'].astype('str') + '_' + total_df['split_time'].astype('str')

mean_df_time_point = total_df.groupby(['split_time']).mean('perc_area')
mean_df_time_point_dict = {i:j for i, j in zip(mean_df_time_point.index, mean_df_time_point.perc_area)}
mean_df_time_point_dict

area_df_time_point = total_df.groupby(['line','split_time']).mean('Area (microm2)').reset_index()
area_df_time_point['line_split'] = area_df_time_point['line'].astype('str') + '_' + area_df_time_point['split_time'].astype('str')
area_df_time_point = {i:j for i, j in zip(area_df_time_point.line_split, area_df_time_point['Area (microm2)'])}
area_df_time_point

total_df['norm_factor'] = total_df.split_time.map(mean_df_time_point_dict)
total_df['perc_area_norm'] = total_df['perc_area'] / total_df['norm_factor']

total_df['mean_area_tp'] = total_df.line_split.map(area_df_time_point)
total_df['area_error'] = (total_df['mean_area_tp'] - total_df['Area (microm2)']) / total_df['Area (microm2)']
total_df['std'] = np.sqrt((total_df['Area (microm2)'] - total_df['mean_area_tp'])**2 / len(total_df))
total_df['cv'] = total_df['std'] / total_df['mean_area_tp']

total_df['line_n_split'] = total_df['line'] + '_' + total_df['n_split'].astype('str')

sns.kdeplot(total_df['cv'])

<AxesSubplot:xlabel='cv', ylabel='Density'>

ax = sns.kdeplot(total_df['area_error'])
ax.axvline(15)

<matplotlib.lines.Line2D at 0x7fe4898dcf10>

ax = sns.kdeplot(total_df['area_error'])
ax.set_xlim(-1, 30)
ax.axvline(10)

<matplotlib.lines.Line2D at 0x7fe4877fc3a0>

fig, ax = plt.subplots(figsize = (20, 10))
sns.scatterplot(data = total_df, y = 'perc_area', x = 'split_time', ax = ax, hue = 'line', palette=line_palette)

<AxesSubplot:xlabel='split_time', ylabel='perc_area'>

total_df = total_df[~((total_df['split_time'] < 25) & (total_df['perc_area'] > 10))]

total_df = total_df[total_df['area_error'] < 5]
total_df.shape

(2170, 25)

idx_max = total_df.groupby('line')['n_split'].idxmax()

# Filter the DataFrame using these indices
filtered_df = total_df.drop(idx_max)
filtered_df

	total_area	perc_area	mean_area_per_colony	n_colonies	time_point	confluency/generation	hour	month	day	line	...	split_time	pixel_size	Area (microm2)	Area (mm2)	line_split	mean_area_tp	area_error	std	cv	line_n_split
CTL04E_3_14_11_1.czi	2532723.0	26.606326	1.266362e+06	2.0	14_11_23_t9	generation	9	11	14	CTL04E	...	159.0	1.38	4.823318e+06	9.185526	CTL04E_159.0	4.827011e+06	0.000766	70.092418	0.000015	CTL04E_3
CTL02A_3_14_11_3.czi	1051145.0	11.042308	1.313931e+05	8.0	14_11_23_t9	generation	9	11	14	CTL02A	...	44.0	1.38	2.001801e+06	3.812229	CTL02A_44.0	2.137034e+06	0.067556	2566.701082	0.001201	CTL02A_3
CHD8WT_3_14_11_1.czi	1655866.0	17.394919	1.655866e+05	10.0	14_11_23_t9	generation	9	11	14	H9	...	44.0	1.38	3.153431e+06	6.005394	H9_44.0	1.326935e+06	-0.579209	34666.426244	0.026125	H9_3
KTD8.2_3_14_11_4.czi	862216.0	9.057603	2.874053e+05	3.0	14_11_23_t9	generation	9	11	14	KTD8.2	...	72.0	1.38	1.642004e+06	3.127033	KTD8.2_72.0	9.805881e+05	-0.402810	12553.504415	0.012802	KTD8.2_3
CTL09A_4_14_11_5.czi	165602.0	1.739654	2.760033e+04	6.0	14_11_23_t9	generation	9	11	14	CTL09A	...	24.0	1.38	3.153724e+05	0.600595	CTL09A_24.0	3.981301e+05	0.262413	1570.719336	0.003945	CTL09A_4
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
CTL08A_5_22_11_2.czi	946317.0	9.941087	6.759407e+04	14.0	22_11_23_t10	generation	10	11	22	CTL08A	...	17.0	1.38	1.802166e+06	3.432045	CTL08A_17.0	2.480685e+06	0.376502	12878.108361	0.005191	CTL08A_5
CTL08A_5_22_11_3.czi	638843.0	6.711064	1.064738e+05	6.0	22_11_23_t10	generation	10	11	22	CTL08A	...	17.0	1.38	1.216613e+06	2.316917	CTL08A_17.0	2.480685e+06	1.039010	23991.761537	0.009671	CTL08A_5
CTL01A_5_22_11_4.czi	834622.0	8.767728	5.961586e+04	14.0	22_11_23_t10	generation	10	11	22	CTL01A	...	17.0	1.38	1.589454e+06	3.026956	CTL01A_17.0	1.876457e+06	0.180567	5447.242123	0.002903	CTL01A_5
CTL08A_5_22_11_4.czi	857634.0	9.009469	1.072042e+05	8.0	22_11_23_t10	generation	10	11	22	CTL08A	...	17.0	1.38	1.633278e+06	3.110415	CTL08A_17.0	2.480685e+06	0.518838	16083.556967	0.006484	CTL08A_5
CHD8WT_5_22_11_1.czi	245495.0	2.578932	1.227475e+05	2.0	22_11_23_t10	generation	10	11	22	H9	...	17.0	1.38	4.675207e+05	0.890346	H9_17.0	2.381361e+06	4.093595	36324.195795	0.015254	H9_5

2151 rows × 25 columns

total_df['logArea'] = np.log10(total_df['Area (microm2)'] + 0.000001)

Growth curves total area - by line

Here we fitted a polynomial regression function of order 3 (exploratory to look at what type of shapes we expect from the curves):

order = total_df.line.unique().tolist()
order.sort()

sns.set_theme(style="ticks")

# Initialize a grid of plots with an Axes for each walk
grid = sns.FacetGrid(total_df.sort_values(by = 'split_time'), col="line", hue = 'line', palette=line_palette,
                     col_wrap=4, height=5, col_order = order)


# Draw a line plot to show the trajectory of each random walk
grid.map(sns.regplot, "split_time", "Area (mm2)", order = 3)

grid.set_axis_labels("Time point post split", "Area (mm2)")

# Adjust the arrangement of the plots
grid.fig.tight_layout(w_pad=1)

Without fitting any regression (line goes through the mean and the highligthed data around is the standard deviation):

sns.set_theme(style="ticks")

# Initialize a grid of plots with an Axes for each walk
grid = sns.FacetGrid(total_df.sort_values(by = 'split_time'), col="line", hue = 'line', palette=line_palette,
                     col_wrap=4, height=5, col_order = order)

# Draw a line plot to show the trajectory of each random walk
grid.map(sns.lineplot, "split_time", "Area (mm2)", markers = True)

grid.set_axis_labels("Time point post split", "Total Area (pixels)")

# Adjust the arrangement of the plots
grid.fig.tight_layout(w_pad=1)

We use the area then average all the FOV for a specific time points in each line. The plot is composed by:

• a solid blue line, that is the smoothed version of this growth curve (using the function gaussian_filter1d from numpy),
• the red around that it is the standard deviation
• the dotted grey line that is the original signal

fig, ax = plt.subplots(4, 3, figsize=(30, 21), gridspec_kw={'hspace': 0.7})
ax = ax.flatten()

for ax_index, line in enumerate(total_df.line.unique()):
    sub = total_df[(total_df.line == line) & (total_df.n_split != 'day')].sort_values(by='datetime')
    mean_st = sub.groupby('split_time')['Area (mm2)'].mean()
    std_st = sub.groupby('split_time')['Area (mm2)'].std()
    y_pos = mean_st.index
    ydata = sub['Area (microm2)'].values
    xdata = sub.split_time.values.astype('int')
    farray = mean_st.values

    # Smoothing
    farray_smooth = gaussian_filter1d(farray, sigma=3)

    # Error formatting
    upper_err = gaussian_filter1d(farray + (std_st / 2).values, sigma=3)
    lower_err = gaussian_filter1d(farray - (std_st / 2).values, sigma=3)

    ax[ax_index].scatter(xdata, ydata)
    ax[ax_index].plot(y_pos, farray, '--', linewidth=0.7, color='k', alpha=0.45)
    ax[ax_index].plot(y_pos, farray_smooth, color='#2374AB')
    ax[ax_index].fill_between(y_pos, upper_err, lower_err, color='crimson', alpha=0.2)

    # Use meaningful limits for better visualization
    ax[ax_index].set_ylim(0, np.max(farray) * 1.25)

    # Rotate x-axis labels for better readability
    ax[ax_index].tick_params(axis='x', rotation=90)

    # Set axis labels and title
    ax[ax_index].set_title(f'Line {line}')
    ax[ax_index].set_ylabel('Total area')
    ax[ax_index].set_xlabel('Time point after split')

plt.tight_layout()  # Adjust layout to prevent overlapping
plt.show()

Growth curves total area - by line and split

Here we fitted a polynomial regression function of order 3:

sns.set_theme(style="ticks")

split_palette = {'1': '#264653', '2': '#2a9d8f', '3': '#8ab17d', '4': '#e9c46a', '5': '#f4a261', '6': '#e76f51'}
line_split_palette = {}

for i in total_df.line_n_split.unique():
    split_n = i.split('_')[-1]
    line_split_palette[i] = split_palette[split_n]

custom_handles = [Line2D([0], [0], color=color, lw=2) for color in split_palette.values()]
grid = sns.FacetGrid(total_df.sort_values(by = 'split_time'), col="line", hue = 'line_n_split', palette=line_split_palette,
                     col_wrap=4, height=5, col_order = order)
grid.map(sns.lineplot, "split_time", "Area (mm2)", markers = True)

grid.add_legend()
if grid._legend:
    grid._legend.remove()  

legend = grid.fig.legend(custom_handles, split_palette.keys(), ncol=2, frameon=False, bbox_to_anchor = (1.2,1), fontsize = 25)

legend.set_title('Passage number', prop={'size': 30})

for ax in grid.axes.flat:
    ax.set_title(ax.get_title(), fontsize=35)

# Increase the size of x and y tick labels
for ax in grid.axes.flat:
    ax.tick_params(axis='x', labelsize=20)
    ax.tick_params(axis='y', labelsize=20)

grid.set_axis_labels("Hours after splitting", "Total area (mm2)", fontsize = 25)
grid.fig.tight_layout(w_pad=1)
grid.fig.savefig('./figures/raw_GC_iPSC_dividedSplit.svg', dpi = 300, bbox_inches = 'tight')

I need to filter out the combination of "line" - "number of split" that do not have enough data point to fit an order 3 polynomial regression:

sns.set_theme(style="ticks")

boolean_sel = pd.Series(total_df.groupby(['line_n_split'])['split_time'].count() > 5)
boolean_sel = boolean_sel[boolean_sel]
filtered_total = total_df[total_df.line_n_split.isin(boolean_sel.index)]

# Initialize a grid of plots with an Axes for each walk
grid = sns.FacetGrid(filtered_total.sort_values(by = 'split_time'), col="line_n_split", hue = 'line', palette=line_palette,
                     col_wrap=4, height=5, col_order = order)

grid.map(sns.regplot, "split_time", "Area (microm2)", order = 3)

# Adjust the arrangement of the plots
grid.fig.tight_layout(w_pad=1)

We use the area then average all the FOV for a specific time points in each line at each split. The plot is composed by:

• a solid blue line, that is the smoothed version of this growth curve (using the function gaussian_filter1d from numpy),
• the red around that it is the standard deviation
• the dotted grey line that is the original signal

fig, ax = plt.subplots(9,5, figsize = (5*10, 7*9), gridspec_kw={'hspace': 0.7})
ax = ax.flatten().T
ax_index = 0
summary_dfs_dict = {}

for l in order:

    sub = total_df[total_df.line == l]
    sub = sub.sort_values(by = 'datetime')
    sub = sub[sub.n_split != 'day']

    splits = sub.n_split.unique().tolist()
    splits.sort()

    for split in splits:

        subsub = sub[sub.n_split == split]

        if len(subsub.split_time.unique()) > 5:
            
            ydata = subsub['Area (microm2)'].values
            xdata = subsub.split_time.values.astype('int')
    
            
            # user defined function,
            # with `area_sum` return the sum of the areas of all the field of view captured for that line at that time point
            summary_df = preprocess(subsub, original_v='Area (microm2)', final_output='mean')

            summary_dfs_dict[f'{l}_split_{split}'] = summary_df
            
            farray = np.array(summary_df['mean'])
    
            y_pos = summary_df.split_time.values
    
            # Smoothing
            farray_smooth = gaussian_filter1d(farray, sigma=3)
    
            # Error formatting
            upper_err = gaussian_filter1d(farray + (summary_df['stds'] / 2), sigma=3)
            lower_err = gaussian_filter1d(farray - (summary_df['stds'] / 2), sigma=3)
    
            ax[ax_index].scatter(xdata, ydata)
            ax[ax_index].plot(y_pos, farray, '--', linewidth=0.7, color='k', alpha=0.45)
            ax[ax_index].plot(y_pos, farray_smooth, color = '#2374AB')
            ax[ax_index].fill_between(y_pos, upper_err, lower_err, color='crimson', alpha=0.2)
            #ax[ax_index].errorbar(y_pos, farray, yerr=summary_df['stds'], fmt='none', color='crimson', alpha=0.5)
            #
            ax[ax_index].set_ylim(0, np.max(farray)+(np.max((farray)*25)/100))
            ax[ax_index].xaxis.set_tick_params(rotation=90)
            ax[ax_index].set_title(f'{l}_split_{split}')
            ax[ax_index].set_ylabel('Total area')
            ax[ax_index].set_xlabel('Time point')
            ax_index += 1
            
        else:
            print(f'Skipped split {subsub.n_split.values[0]} of line {subsub.line.values[0]}')

plt.show()

Skipped split 3 of line CTL01A
Skipped split 1 of line CTL04E
Skipped split 1 of line CTL09A
Skipped split 1 of line UCSFi001-A

Growth curves log total area

We use the logarithm of the area then sum all the FOV for a specific time points in each line at each split. The plot is composed by:

• a solid blue line, that is the smoothed version of this growth curve (using the function gaussian_filter1d from numpy),
• the red around that it is the standard deviation
• the dotted grey line that is the original signal

fig, ax = plt.subplots(10,5, figsize = (5*10, 7*9), gridspec_kw={'hspace': 0.7})
ax = ax.flatten().T
ax_index = 0

for l in order:

    sub = total_df[total_df.line == l]
    sub = sub.sort_values(by = 'datetime')
    sub = sub[sub.n_split != 'day']

    splits = sub.n_split.unique().tolist()
    splits.sort()

    for split in splits:

        subsub = sub[sub.n_split == split]

        
        # user defined function,
        # with `area_sum` return the sum of the areas of all the field of view captured for that line at that time point
        summary_df = preprocess(subsub, original_v='logArea', final_output='area_sum')
        
        farray = np.array(summary_df['area_sum'])

        y_pos = summary_df.datetime.values

        # Smoothing
        farray_smooth = gaussian_filter1d(farray, sigma=1)

        # Error formatting
        upper_err = gaussian_filter1d(farray + (summary_df['stds'] / 2), sigma=1)
        lower_err = gaussian_filter1d(farray - (summary_df['stds'] / 2), sigma=1)

        ax[ax_index].plot(y_pos, farray, '--', linewidth=0.7, color='k', alpha=0.45)
        ax[ax_index].plot(y_pos, farray_smooth, color = '#2374AB')
        ax[ax_index].fill_between(y_pos, upper_err, lower_err, color='crimson', alpha=0.2)
        #
        ax[ax_index].set_ylim(0, np.max(farray)+(np.max((farray)*25)/100))
        ax[ax_index].xaxis.set_tick_params(rotation=90)
        ax[ax_index].set_title(f'{l}_split_{split}')
        ax[ax_index].set_ylabel('Log total area')
        ax[ax_index].set_xlabel('Time point')
        ax_index += 1

plt.show()

lines = total_df.line.unique()

Discrete derivative of the curves - per line per split

We use the total area and then sum all the FOV for a specific time points in each line at each split. Then we smoothed it with gaussian_filter1d and computed the diff, corresponding to the first discrete derivative.

discrete_deriv_curves = {}

fig, ax = plt.subplots(10,5, figsize = (5*10, 7*9), gridspec_kw={'hspace': 0.7})
ax = ax.flatten().T
ax_index = 0

for l in total_df.line.unique():
    
    #color = color_dict[l]

    sub = total_df[total_df.line == l]
    sub = sub.sort_values(by = 'datetime')
    sub = sub[sub.n_split != 'day']

    for split in sub.n_split.unique():

        subsub = sub[sub.n_split == split]

        # user defined function,
        # with `area_sum` return the sum of the areas of all the field of view captured for that line at that time point
        summary_df = preprocess(subsub, original_v='Area (microm2)', final_output='mean')
        
        summary_df = summary_df.sort_values('split_time')
        
        summary_df['smoothed'] = gaussian_filter1d(summary_df['mean'], 3)
        summary_df['derivative'] = summary_df['smoothed'].diff() / summary_df['split_time'].diff()

        discrete_deriv_curves[f'{l}_split_{split}'] = summary_df
        
        farray = np.array(summary_df['derivative'])
        
        y_pos = summary_df.split_time.values
        
        ax[ax_index].errorbar(y_pos, farray, marker = 'o')
        
        ax[ax_index]

        ax[ax_index].xaxis.set_tick_params(rotation=90)
        ax[ax_index].set_title(f'{l}_split_{split}')
        ax[ax_index].set_ylabel('Discrete derivative')
        ax[ax_index].set_xlabel('Time point')
        ax_index += 1
        

plt.show()

Discrete derivative of the curves - per line

We collected the results for each line and each split and we can use it to converge to a single result for each line using as replicates the splits.

deriv_df = pd.concat(discrete_deriv_curves.values(), keys = discrete_deriv_curves.keys()).reset_index()
deriv_df['line'] = deriv_df['level_0'].apply(lambda x: x.split('_')[0])
deriv_df['split'] = deriv_df['level_0'].apply(lambda x: x.split('_')[-1])

fig, ax = plt.subplots(4,3, figsize = (5*4, 7*3), gridspec_kw={'hspace': 0.7})
ax = ax.flatten().T
ax_index = 0

for line in deriv_df.line.unique():
    
    #color = color_dict[l]

    sub = deriv_df[deriv_df.line == line]
    
    sub = sub.sort_values('split_time')

    sub['smoothed'] = gaussian_filter1d(sub['derivative'], sigma = 3)

    sns.lineplot(data = sub, y = 'smoothed', x = 'split_time', hue = 'split', ax = ax[ax_index], markers = True, palette=split_palette)
    ax[ax_index].xaxis.set_tick_params(rotation=90)
    ax[ax_index].set_title(f'{line}')
    ax[ax_index].set_ylabel('Discrete derivative')
    ax[ax_index].set_xlabel('Time point')
    ax_index += 1

fig, ax = plt.subplots(4,3, figsize = (5*4, 7*3)) #, gridspec_kw={'hspace': 0.7})
ax = ax.flatten().T
ax_index = 0

for line in deriv_df.line.unique():
    
    #color = color_dict[l]

    sub = deriv_df[deriv_df.line == line]
    
    sub = sub.sort_values('split_time')

    sub['smoothed'] = gaussian_filter1d(sub['derivative'], sigma = 3)

    sns.lineplot(data = sub, y = 'smoothed', x = 'split_time', ax = ax[ax_index], markers = True, err_style = 'bars')
    ax[ax_index].xaxis.set_tick_params(rotation=90)
    ax[ax_index].set_title(f'{line}')
    ax[ax_index].set_ylabel('Discrete derivative')
    ax[ax_index].set_xlabel('Time point')
    ax_index += 1
    
plt.tight_layout()

Cumulative of the areas - per line per split

We use the total area and then average all the FOV for a specific time points in each line at each split. Then we smoothed it with gaussian_filter1d and computed the cumulative sum over the discrete differential of the growth. with the cumsum() function.

fig, ax = plt.subplots(9,5, figsize = (5*10, 7*9))
ax = ax.flatten().T
ax_index = 0

order_line_n = total_df.line_n_split.unique().tolist()
order_line_n.sort()

for line_n in order_line_n:
    
    sub = total_df[total_df.line_n_split == line_n]
    #sub = sub[~sub.index.duplicated()]
    sub = sub.sort_values('split_time')

    if len(sub.split_time.unique()) > 5:
        
        #sub['smoothed'] = sub.groupby('line_n_split')['Area (microm2)'].apply(gaussian_filter1d, sigma = 3).loc[line_n]
        y = sub.groupby('split_time')['Area (mm2)'].mean().cumsum().values
        x = sub.split_time.unique()
        
        sns.lineplot(y = y, x = x, ax = ax[ax_index], markers = True, err_style='bars')
        ax[ax_index].xaxis.set_tick_params(rotation=90)
        ax[ax_index].set_title(f'{line_n}')
        ax[ax_index].set_ylabel('Cumulative of mean total area')
        ax[ax_index].set_xlabel('Time point')
        ax_index += 1

plt.tight_layout()

sns.set(style="white", palette="Paired", color_codes=True)
fig, ax = plt.subplots(figsize=(7,5))
labels = []
lc = []
handles = []
all_lines = {}

total_df_no_first = total_df[total_df.n_split != '1'].copy()

for l in total_df.line.unique():
    
    color = line_palette[l]

    sub = total_df[total_df.line == l]
    sub = sub.sort_values(by = 'datetime')
    sub = sub[sub.n_split != 'day']

    for split in sub.n_split.unique():

        subsub = sub[sub.n_split == split]

        # user defined function,
        # with `area_sum` return the sum of the areas of all the field of view captured for that line at that time point
        summary_df = preprocess(subsub, original_v='Area (mm2)', final_output='mean')
        
        summary_df = summary_df.sort_values('split_time')
        
        summary_df['smoothed'] = gaussian_filter1d(summary_df['mean'], 1)
        summary_df['cumulative'] = summary_df['smoothed'].cumsum()
        
        farray = np.array(summary_df['cumulative'])
        
        y_pos = summary_df.split_time.values

        line, = ax.plot(y_pos, farray, color = color, marker = '.')
        ax.xaxis.set_tick_params(rotation=90)
        all_lines[f'{l}_{split}'] = line

    labels.append(l)
    handles.append(line)
    lc.append(color)
    
plt.legend(handles, labels, bbox_to_anchor = (1,1))

<matplotlib.legend.Legend at 0x7fe4843eddc0>

lines = total_df.line.unique()

highlight_growth_curves(all_lines, xlabel = 'Hours from split', ylabel = 'Cumulative growth', lines = lines, fontsize = 20)
#plt.savefig('growth_curve_per_line.pdf', dpi = 300)

len(np.float64(list(range(0,200))))

200

fig, ax = plt.subplots(5,9, figsize = (5*12, 8*5))
ax = ax.flatten().T
ax_index = 0

fitted_param = {}

def exp_model(t, a, b, c):
    return a * np.exp(b * t) + c - a

for line_n in order_line_n:

    fitted_param[line_n] = {}
    sub = total_df[total_df.line_n_split == line_n]
    sub = sub.sort_values('split_time')
    
    if len(sub.split_time.unique()) > 5:
        # Calculate the cumulative sum of the mean total area for each split_time
        y = sub.groupby('split_time')['Area (mm2)'].mean().cumsum().values
        y_min_0 = sub[(sub.split_time == sub.split_time.min()) & (sub['Area (mm2)'] > 0)]['Area (mm2)'].min()

        #print(y_min_0)
            
        
        x = np.array(sub.split_time.unique())
        hue = [line_n.split('_')[0]]*len(y)

        try:
            #print(min(y))
            popt, pcov = curve_fit(exp_model, x, y, p0=(min(y), 0.1, y_min_0), bounds=((-np.inf, 0, y_min_0), (np.inf,np.inf, np.inf)))

            fitted_param[line_n]['a'] = popt[0]
            fitted_param[line_n]['rate'] = popt[1]
            fitted_param[line_n]['min(y)'] = min(y)
            fitted_param[line_n]['c'] = popt[2]
            fitted_param[line_n]['mean_cum'] = y
            fitted_param[line_n]['split_time'] = x
            
            a, b, c = popt
            
            # Generate fitted y values
            y_fitted = exp_model(x, a, b, c)
            y_fitted_viz = exp_model(np.float64(list(range(0, 200))), a, b, c)

            fitted_param[line_n]['y_fitted'] = y_fitted
            fitted_param[line_n]['MSLE'] = mean_squared_log_error(y, y_fitted)
            fitted_param[line_n]['r2'] = r2_score(y, y_fitted)
            
            sns.lineplot(y = y_fitted_viz, x = np.float64(list(range(0, 200))), ax = ax[ax_index]) #, markers = True, hue = hue, palette=line_palette, linewidth = 5, legend = None)
            sns.scatterplot(y = y, x = x, ax = ax[ax_index], markers = True, hue = hue, palette=line_palette, s = 150, legend=None)
            #ax[ax_index].xaxis.set_tick_params(rotation=90)
            ax[ax_index].tick_params(axis='both', which='major', labelsize=30)  # Adjust major ticks
            ax[ax_index].tick_params(axis='both', which='minor', labelsize=20)  # Adjust minor ticks
            ax[ax_index].set_title(f'{line_n}', fontsize = 40)
            ax[ax_index].set_ylabel('Cumulative area (mm2)', fontsize = 35)
            ax[ax_index].set_xlabel('Time point', fontsize = 35)
            ax[ax_index].set_xlim(-10, 220)
            ax[ax_index].set_ylim(-10, 250)
            #ax[ax_index].set_xticklabels(ax[ax_index].get_xticklabels(), fontsize = 30)
            #ax[ax_index].set_yticklabels(ax[ax_index].get_yticklabels(), fontsize = 30)
            ax_index += 1
        
        except RuntimeError as e:
            print(f"Fitting failed for line_n {line_n}: {e}")
            
plt.tight_layout()
plt.savefig('./figures/Fitted_cum_area_per_split_new_viz.svg', dpi = 300, bbox_inches = 'tight')

Fitting failed for line_n CTL01A_5: Optimal parameters not found: The maximum number of function evaluations is exceeded.

fig, ax = plt.subplots(5,9, figsize = (5*12, 8*5))
ax = ax.flatten().T
ax_index = 0

fitted_param = {}

def exp_model(t, a, b, c):
    return a * np.exp(b * t) + c - a

for line_n in order_line_n:

    fitted_param[line_n] = {}
    sub = total_df[total_df.line_n_split == line_n]
    sub = sub.sort_values('split_time')
    
    if len(sub.split_time.unique()) > 5:
        # Calculate the cumulative sum of the mean total area for each split_time
        y = sub.groupby('split_time')['Area (mm2)'].mean().cumsum().values
        y_min_0 = sub[(sub.split_time == sub.split_time.min()) & (sub['Area (mm2)'] > 0)]['Area (mm2)'].min()

        #print(y_min_0)
            
        
        x = np.array(sub.split_time.unique())
        hue = [line_n.split('_')[0]]*len(y)

        try:
            #print(min(y))
            popt, pcov = curve_fit(exp_model, x, y, p0=(min(y), 0.1, y_min_0), bounds=((-np.inf, 0, y_min_0), (np.inf,np.inf, np.inf)))

            fitted_param[line_n]['a'] = popt[0]
            fitted_param[line_n]['rate'] = popt[1]
            fitted_param[line_n]['min(y)'] = min(y)
            fitted_param[line_n]['c'] = popt[2]
            fitted_param[line_n]['mean_cum'] = y
            fitted_param[line_n]['split_time'] = x
            
            a, b, c = popt
            
            # Generate fitted y values
            y_fitted = exp_model(x, a, b, c)
            y_fitted_viz = exp_model(np.float64(list(range(0, 200))), a, b, c)

            fitted_param[line_n]['y_fitted'] = y_fitted
            #fitted_param[line_n]['MSLE'] = mean_squared_log_error(y, y_fitted)
            fitted_param[line_n]['r2'] = r2_score(y, y_fitted)
            
            sns.lineplot(y = y_fitted, x = x, ax = ax[ax_index], markers = True, hue = hue, palette=line_palette, linewidth = 5, legend = None)
            sns.scatterplot(y = y, x = x, ax = ax[ax_index], markers = True, hue = hue, palette=line_palette, s = 150, legend=None)
            ax[ax_index].xaxis.set_tick_params(rotation=90)
            ax[ax_index].set_title(f'{line_n}', fontsize = 40)
            ax[ax_index].set_ylabel('Cumulative area (mm2)', fontsize = 35)
            ax[ax_index].set_xlabel('Time point', fontsize = 35)
            #ax[ax_index].set_xlim(-10, 220)
            #ax[ax_index].set_ylim(-10, 85000)
            _ = ax[ax_index].set_xticklabels(ax[ax_index].get_xticklabels(), fontsize = 30)
            _ = ax[ax_index].set_yticklabels(ax[ax_index].get_yticklabels(), fontsize = 30)
            ax_index += 1
        
        except RuntimeError as e:
            print(f"Fitting failed for line_n {line_n}: {e}")
            
plt.tight_layout()
#plt.savefig('./figures/Fitted_cum_area_per_split_orig_viz.svg', dpi = 300, bbox_inches = 'tight')

Fitting failed for line_n CTL01A_5: Optimal parameters not found: The maximum number of function evaluations is exceeded.

donor_map_names = {i:j for i, j in zip(total_df['line'], total_df['line'])}
donor_map_names['CHD2WT'] = 'UCSFi001-A'
donor_map_names['CHD8WT'] = 'H9'
donor_map_names['CTL01A'] = 'CTL01'
total_df['line'] = total_df['line'].map(donor_map_names)
total_df['line_n_split'] = total_df['line'] + '_' + total_df['n_split'].astype('str')
order_line_n = total_df.line_n_split.unique().tolist()
order_line_n.sort()

line_palette = {'CTL01': '#DBB807',
 'CTL08A': '#0FB248',
 'CTL04E': '#FF0054',
 'CTL02A': '#7B00FF',
 'H9': '#72190E',
 'H1': '#994F88',
 'CTL05A': '#1965B0',
 'CTL07C': '#437DBF',
 'CTL06F': '#CAE0AB',
 'CTL09A': '#FFFF00',
 'KTD8.2': '#E65518',
 'UCSFi001-A': '#7BAFDE'}

fig, ax = plt.subplots(5,9, figsize = (5*12, 8*5))
ax = ax.flatten().T
ax_index = 0

fitted_param = {}

def exp_model(t, a, b, c, d):
    return a * np.exp(b * (t + d)) + c - a

for line_n in order_line_n:

    fitted_param[line_n] = {}
    sub = total_df[total_df.line_n_split == line_n]
    sub = sub.sort_values('split_time')
    
    if len(sub.split_time.unique()) > 5:
        # Calculate the cumulative sum of the mean total area for each split_time
        y = sub.groupby('split_time')['Area (mm2)'].mean().cumsum().values
        y_min_0 = sub[(sub.split_time == sub.split_time.min()) & (sub['Area (mm2)'] > 0)]['Area (mm2)'].min()

        #print(y_min_0)
            
        
        x = np.array(sub.split_time.unique())
        hue = [line_n.split('_')[0]]*len(y)

        try:
            #print(min(y))
            popt, pcov = curve_fit(exp_model, x, y, p0=(min(y), 0.1, y_min_0, 0), bounds=((-np.inf, 0, y_min_0, 0), (np.inf,np.inf, np.inf, np.inf)))

            fitted_param[line_n]['a'] = popt[0]
            fitted_param[line_n]['rate'] = popt[1]
            fitted_param[line_n]['min(y)'] = min(y)
            fitted_param[line_n]['c'] = popt[2]
            fitted_param[line_n]['d'] = popt[3]
            fitted_param[line_n]['mean_cum'] = y
            fitted_param[line_n]['split_time'] = x
            
            a, b, c, d = popt
            
            # Generate fitted y values
            y_fitted = exp_model(x, a, b, c, d)
            y_fitted_viz = exp_model(np.float64(list(range(0, 200))), a, b, c, d)

            fitted_param[line_n]['y_fitted'] = y_fitted
            #fitted_param[line_n]['MSLE'] = mean_squared_log_error(y, y_fitted)
            fitted_param[line_n]['r2'] = r2_score(y, y_fitted)
            
            sns.lineplot(y = y_fitted_viz, x = np.float64(list(range(0, 200))), ax = ax[ax_index]) #, markers = True, hue = hue, palette=line_palette, linewidth = 5, legend = None)
            sns.scatterplot(y = y, x = x, ax = ax[ax_index], markers = True, hue = hue, palette=line_palette, s = 150, legend=None)
            ax[ax_index].xaxis.set_tick_params(rotation=90)
            ax[ax_index].set_title(f'{line_n}', fontsize = 40)
            ax[ax_index].set_ylabel('Cumulative area (mm2)', fontsize = 35)
            ax[ax_index].set_xlabel('Time point', fontsize = 35)
            ax[ax_index].set_xlim(-10, 220)
            ax[ax_index].set_ylim(-10, 250)
            _ = ax[ax_index].set_xticklabels(ax[ax_index].get_xticklabels(), fontsize = 30)
            _ = ax[ax_index].set_yticklabels(ax[ax_index].get_yticklabels(), fontsize = 30)
            ax_index += 1
        
        except RuntimeError as e:
            print(f"Fitting failed for line_n {line_n}: {e}")
            
plt.tight_layout()
#plt.savefig('./figures/Fitted_cum_area_per_split_new_viz_new_name.svg', dpi = 300, bbox_inches = 'tight')

fitted_df = pd.DataFrame.from_dict(fitted_param).T
fitted_df['Line'] = fitted_df.reset_index()['index'].apply(lambda x: x.split('_')[0]).values
fitted_df['split'] = fitted_df.reset_index()['index'].apply(lambda x: x.split('_')[1]).values
fitted_df = fitted_df[~fitted_df.a.isna()]
fitted_df['a+c'] = fitted_df['a'] + fitted_df['c']
fitted_df

	a	rate	min(y)	c	d	mean_cum	split_time	y_fitted	r2	Line	split	a+c
CTL01_2	0.140842	0.031439	0.128738	0.051989	0.0	[0.12873836706191996, 0.5126940096263999, 0.75...	[49.0, 57.0, 72.0, 81.0, 96.0, 105.0, 120.0]	[0.5684554397560638, 0.7564249822784911, 1.265...	0.955038	CTL01	2	0.192832
CTL01_4	6.709435	0.020925	1.071547	0.93823	0.0	[1.0715473444571997, 1.7103960320254554, 3.865...	[0.0, 8.0, 25.0, 33.0, 48.0, 56.0, 73.0]	[0.938230218953283, 2.160852939749881, 5.54949...	0.958803	CTL01	4	7.647666
CTL01_5	186.079023	0.000661	1.015545	1.016249	1.889604	[1.0155450486297597, 1.5641046091350714, 4.591...	[0.0, 16.0, 17.0, 24.0, 39.0, 48.0, 63.0]	[1.2487270333315053, 3.228882692965442, 3.3533...	0.886366	CTL01	5	187.095273
CTL02A_1	1.35829	0.02225	1.065226	0.550477	0.0	[1.0652259377527198, 1.4048785412085596, 2.313...	[39.0, 48.0, 63.0, 72.0, 88.0, 96.0, 111.0, 12...	[2.4269678603212426, 3.1441310003253333, 4.709...	0.974893	CTL02A	1	1.908767
CTL02A_2	0.954612	0.043378	1.26411	0.76608	0.0	[1.2641101587982075, 1.7939214715189675, 4.596...	[15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0, 96.0]	[1.6412790235890737, 2.5151392616598383, 4.993...	0.992677	CTL02A	2	1.720692
CTL02A_3	16.613952	0.016347	1.649741	0.656578	0.0	[1.6497408713817594, 2.607119548807967, 3.9639...	[0.0, 5.0, 20.0, 29.0, 44.0, 52.0, 68.0, 76.0,...	[0.6565776408130546, 2.0715333228559345, 7.081...	0.975446	CTL02A	3	17.27053
CTL02A_5	0.682361	0.037966	0.654197	0.588409	0.0	[0.6541966858658399, 0.9161832703838398, 1.754...	[0.0, 16.0, 24.0, 39.0, 48.0, 63.0]	[0.58840944724512, 1.158686195549207, 1.603241...	0.983085	CTL02A	5	1.27077
CTL04E_2	0.821181	0.024744	0.299609	0.299609	0.0	[0.2996085652689599, 1.1036059070299196, 1.703...	[24.0, 33.0, 49.0, 57.0, 72.0, 81.0, 96.0, 105...	[0.9655543682098432, 1.3365054988339438, 2.239...	0.985605	CTL04E	2	1.120789
CTL04E_3	1.306327	0.023063	2.123347	2.123347	0.0	[2.1233470930991993, 2.4315673509784794, 2.677...	[15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0, 96....	[2.66327926587685, 3.089170751678419, 4.028297...	0.976291	CTL04E	3	3.429674
CTL04E_4	9.612778	0.017852	1.218989	0.859733	0.0	[1.2189894108551995, 2.1238454675329193, 2.880...	[0.0, 8.0, 25.0, 33.0, 48.0, 56.0, 73.0, 81.0,...	[0.8597330722492273, 2.3354356093880746, 6.266...	0.990038	CTL04E	4	10.472511
CTL04E_5	2.962125	0.037622	1.656866	0.84359	0.0	[1.6568662053110392, 2.247560498352959, 2.5440...	[0.0, 16.0, 24.0, 39.0, 48.0, 63.0]	[0.8435904553541462, 3.2893968997575933, 5.188...	0.835627	CTL04E	5	3.805716
CTL05A_1	0.831961	0.030813	0.779193	0.497694	0.0	[0.7791926205821758, 2.426386553802719, 4.5256...	[39.0, 48.0, 63.0, 72.0, 88.0, 96.0, 111.0, 12...	[2.432703584024785, 3.3169982345469524, 5.4623...	0.99813	CTL05A	1	1.329655
CTL05A_2	0.055171	0.043012	0.205236	0.490657	0.192915	[0.20523627369755992, 0.5079725389905838, 0.63...	[9.0, 24.0, 33.0, 48.0, 59.0, 72.0, 81.0, 96.0...	[0.5174144971958101, 0.5916686668561622, 0.665...	0.999672	CTL05A	2	0.545828
CTL05A_3	2.543078	0.01896	1.430206	0.870664	0.0	[1.4302055733008394, 1.6829849546056073, 1.766...	[0.0, 15.0, 23.0, 39.0, 47.0, 64.0, 72.0, 87.0...	[0.8706640646764798, 1.7072361489421515, 2.260...	0.984739	CTL05A	3	3.413742
CTL06F_1	0.192261	0.038794	0.186632	0.149139	0.0	[0.18663200746559994, 0.5037948979217999, 0.99...	[0.0, 39.0, 48.0, 63.0, 72.0, 88.0, 96.0, 111....	[0.14913877596192965, 0.8297827985903414, 1.19...	0.998507	CTL06F	1	0.341399
CTL06F_2	0.178737	0.048632	0.221248	0.603456	0.025076	[0.22124802574367994, 0.5315105005565759, 0.98...	[0.0, 9.0, 24.0, 33.0, 48.0, 59.0, 72.0, 81.0,...	[0.6036744948519198, 0.7019439338747042, 0.999...	0.998732	CTL06F	2	0.782194
CTL06F_3	9.10152	0.017721	0.835248	0.584532	0.0	[0.8352482294782076, 1.4114732831694714, 2.609...	[0.0, 5.0, 20.0, 29.0, 44.0, 52.0, 68.0, 76.0,...	[0.5845324628693156, 1.4277887490358108, 4.455...	0.9908	CTL06F	3	9.686052
CTL06F_5	1.440098	0.028446	0.995236	1.003616	1.829151	[0.9952359126703195, 2.065253135791535, 2.6851...	[0.0, 16.0, 24.0, 39.0, 48.0, 63.0]	[1.0805315559824449, 1.9549254566209664, 2.566...	0.996178	CTL06F	5	2.443714
CTL07C_2	0.247166	0.031126	0.098445	0.039209	0.0	[0.09844493853571196, 0.27541168560691187, 0.4...	[9.0, 24.0, 33.0, 49.0, 57.0, 72.0, 81.0, 96.0...	[0.11911823212082312, 0.31373406544445276, 0.4...	0.990575	CTL07C	2	0.286375
CTL07C_3	1.574502	0.035564	2.400426	2.022206	0.689164	[2.400426353463839, 3.2856292908866864, 4.3438...	[0.0, 15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0]	[2.061272905633547, 3.198562502772172, 4.23628...	0.998319	CTL07C	3	3.596708
CTL07C_4	6.062433	0.019101	0.478994	0.409045	0.0	[0.47899434749327985, 0.8008914021730558, 1.50...	[0.0, 5.0, 20.0, 29.0, 44.0, 52.0, 68.0, 76.0,...	[0.409045425456962, 1.016575988537614, 3.22947...	0.978949	CTL07C	4	6.471478
CTL07C_6	2.86121	0.030355	0.717828	0.424542	0.0	[0.7178284323935998, 1.3666883712911995, 2.714...	[0.0, 16.0, 24.0, 39.0, 48.0, 63.0]	[0.4245424828464115, 2.2135806392001545, 3.491...	0.982106	CTL07C	6	3.285752
CTL08A_1	1.187041	0.033521	0.33419	0.103732	0.0	[0.33418952506655986, 1.1351766731587196, 3.25...	[0.0, 39.0, 48.0, 63.0, 72.0, 88.0, 96.0, 111.0]	[0.10373199917488773, 3.3042502170853707, 4.84...	0.980946	CTL08A	1	1.290773
CTL08A_2	0.706487	0.033213	0.165209	0.120179	0.0	[0.16520885806607996, 0.42682587784329584, 0.6...	[0.0, 15.0, 24.0, 39.0, 48.0, 63.0, 72.0, 87.0...	[0.12017926217232122, 0.5763852017201965, 0.98...	0.996042	CTL08A	2	0.826666
CTL08A_3	4.495583	0.021725	0.369839	0.164502	0.0	[0.3698385596056799, 0.6810055432149598, 1.573...	[0.0, 5.0, 20.0, 29.0, 44.0, 52.0, 68.0, 76.0,...	[0.1645016438908815, 0.6803478200863058, 2.610...	0.973682	CTL08A	3	4.660084
CTL08A_5	29.785332	0.003436	0.718488	0.314723	3.941521	[0.7184884989571197, 0.8260278491119677, 3.779...	[0.0, 16.0, 17.0, 24.0, 39.0, 48.0, 63.0]	[0.7208531458460676, 2.4271380041338624, 2.536...	0.886176	CTL08A	5	30.100055
CTL09A_2	0.263506	0.036516	0.416052	0.326098	0.0	[0.41605228590047993, 0.8020691253345598, 1.64...	[33.0, 49.0, 57.0, 72.0, 81.0, 96.0, 105.0, 12...	[0.9418803460915361, 1.6397387847215783, 2.174...	0.9842	CTL09A	2	0.589604
CTL09A_3	2.677791	0.028298	1.09468	0.4693	0.0	[1.0946797761170877, 2.2220952270454073, 3.557...	[15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0, 96....	[1.8852783759737175, 3.0726940265447356, 5.865...	0.98176	CTL09A	3	3.147091
CTL09A_4	3.743789	0.024477	0.856375	0.856375	0.0	[0.8563747115980797, 1.4846659608893753, 2.637...	[9.0, 24.0, 32.0, 48.0, 56.0, 73.0, 81.0, 96.0...	[1.7789881436924095, 3.8490741088358766, 5.306...	0.990837	CTL09A	4	4.600164
CTL09A_5	0.63178	0.044788	0.999207	1.358836	0.463645	[0.9992065878129598, 1.4917047366392635, 2.493...	[0.0, 8.0, 24.0, 32.0, 47.0, 56.0, 71.0]	[1.3720928133032406, 1.650041365050099, 2.6168...	0.98726	CTL09A	5	1.990617
H1_1	0.881927	0.022767	0.127647	0.032898	0.0	[0.12764744386243193, 0.2877317192128319, 0.33...	[9.0, 24.0, 33.0, 48.0, 57.0, 72.0, 83.0, 96.0...	[0.23345521211899467, 0.6740987835864768, 1.02...	0.98154	H1	1	0.914825
H1_2	4.602872	0.013332	2.472889	2.472889	0.0	[2.4728886058766393, 2.915316716446655, 3.1268...	[0.0, 15.0, 39.0, 47.0, 64.0, 72.0, 87.0, 95.0...	[2.4728886059932584, 3.4919010775579657, 5.611...	0.957078	H1	2	7.07576
H9_1	4.27921	0.024254	0.377707	0.350742	0.0	[0.3777067706471999, 0.9652240400097598, 2.490...	[0.0, 15.0, 24.0, 40.0, 48.0, 63.0, 72.0, 87.0...	[0.35074196362019805, 2.228442590313313, 3.730...	0.986148	H9	1	4.629952
H9_2	0.659132	0.045415	0.301872	0.153647	0.0	[0.30187165062959986, 1.850863636851551, 3.155...	[15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0]	[0.7971585634024018, 1.4548830572822027, 3.368...	0.999084	H9	2	0.812778
H9_3	11.484073	0.015581	0.90592	0.3021	0.0	[0.9059195979950396, 1.1298801829973755, 1.425...	[0.0, 5.0, 20.0, 29.0, 44.0, 52.0, 68.0, 76.0,...	[0.30210013531553237, 1.232548066656026, 4.501...	0.975495	H9	3	11.786173
H9_5	1.240493	0.023808	0.809685	0.730269	0.791928	[0.8096849757622797, 0.9034534152302397, 1.793...	[0.0, 16.0, 17.0, 39.0, 48.0, 63.0]	[0.7538788914698014, 1.3399635667979695, 1.384...	0.965619	H9	5	1.970761
KTD8.2_1	0.238791	0.041092	0.550485	0.550485	0.0	[0.5504846337575998, 0.9347023082408397, 1.524...	[0.0, 39.0, 48.0, 63.0, 72.0, 88.0, 96.0, 111.0]	[0.5504846337576003, 1.4975103321043415, 2.028...	0.986486	KTD8.2	1	0.789275
KTD8.2_2	0.367678	0.039801	0.713858	1.743854	0.6572	[0.7138583617075197, 1.1289241745020795, 3.124...	[0.0, 15.0, 24.0, 39.0, 48.0, 63.0, 72.0, 87.0...	[1.753597797333993, 2.061830036541058, 2.35718...	0.987279	KTD8.2	2	2.111532
KTD8.2_3	2.067122	0.018607	0.107452	0.056472	0.0	[0.10745158306233597, 0.3914869295194559, 0.60...	[9.0, 28.0, 33.0, 48.0, 57.0, 72.0, 80.0, 96.0...	[0.43331855893314675, 1.4698024054174912, 1.80...	0.988663	KTD8.2	3	2.123594
KTD8.2_4	1.686085	0.026211	1.417346	1.344326	0.062617	[1.4173458607295994, 2.1666846135959994, 2.887...	[0.0, 16.0, 24.0, 39.0, 48.0, 63.0]	[1.3470955115139647, 2.2270197490582477, 2.826...	0.987125	KTD8.2	4	3.030411
UCSFi001-A_2	0.588666	0.026581	0.470745	0.461125	0.0	[0.4707453288189598, 1.1102174528831996, 1.745...	[24.0, 33.0, 49.0, 57.0, 72.0, 81.0, 96.0, 105...	[0.9865637008725591, 1.2876735624447133, 2.037...	0.970674	UCSFi001-A	2	1.049792
UCSFi001-A_3	1.067307	0.025661	0.823938	0.73609	0.0	[0.8239383636753597, 1.0375904860577996, 1.344...	[0.0, 15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0...	[0.7360902739843218, 1.2371895963042165, 1.644...	0.995604	UCSFi001-A	3	1.803397
UCSFi001-A_4	11.891798	0.016863	0.65714	0.65714	0.0	[0.6571397848564797, 1.3643807979277436, 3.360...	[0.0, 8.0, 25.0, 33.0, 48.0, 56.0, 73.0, 81.0,...	[0.6571397848586606, 2.3746568201900295, 6.892...	0.99402	UCSFi001-A	4	12.548938
UCSFi001-A_5	0.695858	0.055867	1.776417	1.328369	0.0	[1.7764168326609595, 2.3372079343318073, 3.079...	[0.0, 16.0, 24.0, 39.0, 48.0, 63.0]	[1.3283694521265619, 2.3335912072530425, 3.292...	0.981117	UCSFi001-A	5	2.024227

donor_map_names = {i:j for i, j in zip(total_df['line'], total_df['line'])}
donor_map_names['CHD2WT'] = 'UCSFi001-A'
donor_map_names['CHD8WT'] = 'H9'
donor_map_names['CTL01'] = 'CTL01A'
total_df['line'] = total_df['line'].map(donor_map_names)
total_df['line_n_split'] = total_df['line'] + '_' + total_df['n_split'].astype('str')
order_line_n = total_df.line_n_split.unique().tolist()
order_line_n.sort()

line_palette = {'CTL01A': '#DBB807',
 'CTL08A': '#0FB248',
 'CTL04E': '#FF0054',
 'CTL02A': '#7B00FF',
 'H9': '#72190E',
 'H1': '#994F88',
 'CTL05A': '#1965B0',
 'CTL07C': '#437DBF',
 'CTL06F': '#CAE0AB',
 'CTL09A': '#FFFF00',
 'KTD8.2': '#E65518',
 'UCSFi001-A': '#7BAFDE'}

fig, ax = plt.subplots(5,9, figsize = (5*12, 8*5))
ax = ax.flatten().T
ax_index = 0

fitted_param = {}

def exp_model(t, a, b, c):
    return a * np.exp(b * t) + c - a

for line_n in order_line_n:

    fitted_param[line_n] = {}
    sub = total_df[total_df.line_n_split == line_n]
    sub = sub.sort_values('split_time')
    
    if len(sub.split_time.unique()) > 5:
        # Calculate the cumulative sum of the mean total area for each split_time
        y = sub.groupby('split_time')['Area (mm2)'].mean().cumsum().values
        y_min_0 = sub[(sub.split_time == sub.split_time.min()) & (sub['Area (mm2)'] > 0)]['Area (mm2)'].min()

        #print(y_min_0)
            
        
        x = np.array(sub.split_time.unique())
        hue = [line_n.split('_')[0]]*len(y)

        try:
            #print(min(y))
            popt, pcov = curve_fit(exp_model, x, y, p0=(min(y), 0.1, y_min_0), bounds=((-np.inf, 0, y_min_0), (np.inf,np.inf, np.inf)))

            fitted_param[line_n]['a'] = popt[0]
            fitted_param[line_n]['rate'] = popt[1]
            fitted_param[line_n]['min(y)'] = min(y)
            fitted_param[line_n]['c'] = popt[2]
            fitted_param[line_n]['mean_cum'] = y
            fitted_param[line_n]['split_time'] = x
            
            a, b, c = popt
            
            # Generate fitted y values
            y_fitted = exp_model(x, a, b, c)
            y_fitted_viz = exp_model(np.float64(list(range(0, 200))), a, b, c)

            fitted_param[line_n]['y_fitted'] = y_fitted
            fitted_param[line_n]['MSLE'] = mean_squared_log_error(y, y_fitted)
            fitted_param[line_n]['r2'] = r2_score(y, y_fitted)
            
            sns.lineplot(y = y_fitted, x = x, ax = ax[ax_index], markers = True, hue = hue, palette=line_palette, linewidth = 5, legend = None)
            sns.scatterplot(y = y, x = x, ax = ax[ax_index], markers = True, hue = hue, palette=line_palette, s = 150, legend=None)
            ax[ax_index].xaxis.set_tick_params(rotation=90)
            ax[ax_index].set_title(f'{line_n}', fontsize = 40)
            ax[ax_index].set_ylabel('Cumulative area (mm2)', fontsize = 35)
            ax[ax_index].set_xlabel('Time point', fontsize = 35)
            #ax[ax_index].set_xlim(-10, 220)
            #ax[ax_index].set_ylim(-10, 85000)
            _ = ax[ax_index].set_xticklabels(ax[ax_index].get_xticklabels(), fontsize = 30)
            _ = ax[ax_index].set_yticklabels(ax[ax_index].get_yticklabels(), fontsize = 30)
            ax_index += 1
        
        except RuntimeError as e:
            print(f"Fitting failed for line_n {line_n}: {e}")
            
plt.tight_layout()
#plt.savefig('./figures/Fitted_cum_area_per_split_orig_viz_new_name.svg', dpi = 300, bbox_inches = 'tight')

Fitting failed for line_n CTL01A_5: Optimal parameters not found: The maximum number of function evaluations is exceeded.

sns.set(style="white", palette="Paired", color_codes=True)
fig, ax = plt.subplots(figsize=(7,5))
labels = []
lc = []
handles = []
all_lines = {}

total_df_no_first = total_df[total_df.n_split != '1'].copy()

for l in total_df.line.unique():
    
    color = line_palette[l]

    sub = total_df[total_df.line == l]
    sub = sub.sort_values(by = 'datetime')
    sub = sub[sub.n_split != 'day']

    for split in sub.n_split.unique():


        subsub = sub[sub.n_split == split]

        if len(subsub.split_time.unique()) > 5:

            # user defined function,
            # with `area_sum` return the sum of the areas of all the field of view captured for that line at that time point
            summary_df = preprocess(subsub, original_v='Area (mm2)', final_output='mean')
            
            summary_df = summary_df.sort_values('split_time')
            summary_df['cumulative'] = summary_df['mean'].cumsum()
            
            farray = np.array(summary_df['cumulative'].values)
            y_pos = summary_df.split_time.values
    
            popt, pcov = curve_fit(exp_model, y_pos, farray, p0=(max(farray), 0.1, 0))
            
            a, b, c = popt
    
            y_fitted = exp_model(y_pos, a, b, c)
    
            line, = ax.plot(y_pos, y_fitted, color = color, marker = '.')
            ax.xaxis.set_tick_params(rotation=90)
            all_lines[f'{l}_{split}'] = line
    
        labels.append(l)
        handles.append(line)
        lc.append(color)
    
plt.legend(handles, labels, bbox_to_anchor = (1,1))

<matplotlib.legend.Legend at 0x7fe484fef520>

lines = total_df.line.unique()

highlight_growth_curves(all_lines, xlabel = 'Hours from split', ylabel = 'Cumulative area (mm2)', lines = lines, fontsize = 20)
#plt.savefig('./figures/cumulative_growth_curve_per_line.svg', dpi = 300)

fitted_df = pd.DataFrame.from_dict(fitted_param).T
fitted_df['Line'] = fitted_df.reset_index()['index'].apply(lambda x: x.split('_')[0]).values
fitted_df['split'] = fitted_df.reset_index()['index'].apply(lambda x: x.split('_')[1]).values
fitted_df = fitted_df[~fitted_df.a.isna()]
fitted_df['a+c'] = fitted_df['a'] + fitted_df['c']

fitted_df[fitted_df['a+c'] > 0].shape

(43, 12)

fitted_df

	a	rate	min(y)	c	mean_cum	split_time	y_fitted	MSLE	r2	Line	split	a+c
CTL01A_2	0.140845	0.031439	0.128738	0.051989	[0.12873836706191996, 0.5126940096263999, 0.75...	[49.0, 57.0, 72.0, 81.0, 96.0, 105.0, 120.0]	[0.5684601783697514, 0.7564306877808943, 1.265...	0.033141	0.955038	CTL01A	2	0.192835
CTL01A_4	6.709435	0.020925	1.071547	0.93823	[1.0715473444571997, 1.7103960320254554, 3.865...	[0.0, 8.0, 25.0, 33.0, 48.0, 56.0, 73.0]	[0.9382302189532821, 2.1608528979695825, 5.549...	0.024887	0.958803	CTL01A	4	7.647665
CTL02A_1	1.358287	0.02225	1.065226	0.550477	[1.0652259377527198, 1.4048785412085596, 2.313...	[39.0, 48.0, 63.0, 72.0, 88.0, 96.0, 111.0, 12...	[2.4269662693898706, 3.144128958826294, 4.7098...	0.10339	0.974893	CTL02A	1	1.908765
CTL02A_2	0.954612	0.043378	1.26411	0.76608	[1.2641101587982075, 1.7939214715189675, 4.596...	[15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0, 96.0]	[1.6412790277239497, 2.5151392692655543, 4.993...	0.016467	0.992677	CTL02A	2	1.720692
CTL02A_3	16.613953	0.016347	1.649741	0.656578	[1.6497408713817594, 2.607119548807967, 3.9639...	[0.0, 5.0, 20.0, 29.0, 44.0, 52.0, 68.0, 76.0,...	[0.6565776402558363, 2.0715333393022206, 7.081...	0.11749	0.975446	CTL02A	3	17.27053
CTL02A_5	0.682361	0.037966	0.654197	0.588409	[0.6541966858658399, 0.9161832703838398, 1.754...	[0.0, 16.0, 24.0, 39.0, 48.0, 63.0]	[0.5884094472451199, 1.1586862058833431, 1.603...	0.007286	0.983085	CTL02A	5	1.27077
CTL04E_2	0.821185	0.024744	0.299609	0.299609	[0.2996085652689599, 1.1036059070299196, 1.703...	[24.0, 33.0, 49.0, 57.0, 72.0, 81.0, 96.0, 105...	[0.9655562584883766, 1.3365081793448954, 2.239...	0.028769	0.985605	CTL04E	2	1.120794
CTL04E_3	1.306325	0.023063	2.123347	2.123347	[2.1233470930991993, 2.4315673509784794, 2.677...	[15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0, 96....	[2.6632786987130626, 3.089169790618284, 4.0282...	0.068529	0.976291	CTL04E	3	3.429672
CTL04E_4	9.612778	0.017852	1.218989	0.859733	[1.2189894108551995, 2.1238454675329193, 2.880...	[0.0, 8.0, 25.0, 33.0, 48.0, 56.0, 73.0, 81.0,...	[0.8597330722454402, 2.3354356000019507, 6.266...	0.044278	0.990038	CTL04E	4	10.472511
CTL04E_5	2.962251	0.037622	1.656866	0.84359	[1.6568662053110392, 2.247560498352959, 2.5440...	[0.0, 16.0, 24.0, 39.0, 48.0, 63.0]	[0.8435904553543887, 3.289444280042749, 5.1886...	0.200981	0.835627	CTL04E	5	3.805842
CTL05A_1	0.831961	0.030813	0.779193	0.497694	[0.7791926205821758, 2.426386553802719, 4.5256...	[39.0, 48.0, 63.0, 72.0, 88.0, 96.0, 111.0, 12...	[2.432703578982128, 3.3169982277731034, 5.4623...	0.052295	0.99813	CTL05A	1	1.329655
CTL05A_2	0.055631	0.043012	0.205236	0.491117	[0.20523627369755992, 0.5079725389905838, 0.63...	[9.0, 24.0, 33.0, 48.0, 59.0, 72.0, 81.0, 96.0...	[0.5174145386527128, 0.5916687051661024, 0.665...	0.00577	0.999672	CTL05A	2	0.546748
CTL05A_3	2.543079	0.01896	1.430206	0.870664	[1.4302055733008394, 1.6829849546056073, 1.766...	[0.0, 15.0, 23.0, 39.0, 47.0, 64.0, 72.0, 87.0...	[0.8706640646764798, 1.7072362370661094, 2.260...	0.079341	0.984739	CTL05A	3	3.413743
CTL06F_1	0.192261	0.038794	0.186632	0.149139	[0.18663200746559994, 0.5037948979217999, 0.99...	[0.0, 39.0, 48.0, 63.0, 72.0, 88.0, 96.0, 111....	[0.14913877596194025, 0.8297829559442185, 1.19...	0.008407	0.998507	CTL06F	1	0.3414
CTL06F_2	0.178955	0.048632	0.221248	0.603675	[0.22124802574367994, 0.5315105005565759, 0.98...	[0.0, 9.0, 24.0, 33.0, 48.0, 59.0, 72.0, 81.0,...	[0.6036745082056189, 0.701943955589503, 0.9996...	0.014467	0.998732	CTL06F	2	0.78263
CTL06F_3	9.101519	0.017721	0.835248	0.584532	[0.8352482294782076, 1.4114732831694714, 2.609...	[0.0, 5.0, 20.0, 29.0, 44.0, 52.0, 68.0, 76.0,...	[0.5845324628693316, 1.4277887166726817, 4.455...	0.035992	0.9908	CTL06F	3	9.686051
CTL06F_5	1.517014	0.028446	0.995236	1.080533	[0.9952359126703195, 2.065253135791535, 2.6851...	[0.0, 16.0, 24.0, 39.0, 48.0, 63.0]	[1.0805325124857454, 1.9549269947108237, 2.566...	0.001386	0.996178	CTL06F	5	2.597547
CTL07C_2	0.247166	0.031126	0.098445	0.039209	[0.09844493853571196, 0.27541168560691187, 0.4...	[9.0, 24.0, 33.0, 49.0, 57.0, 72.0, 81.0, 96.0...	[0.11911823217794204, 0.31373406561857875, 0.4...	0.004426	0.990575	CTL07C	2	0.286375
CTL07C_3	1.613569	0.035564	2.400426	2.061275	[2.400426353463839, 3.2856292908866864, 4.3438...	[0.0, 15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0]	[2.0612745335144926, 3.198564283424051, 4.2362...	0.003228	0.998319	CTL07C	3	3.674844
CTL07C_4	6.062421	0.019101	0.478994	0.409045	[0.47899434749327985, 0.8008914021730558, 1.50...	[0.0, 5.0, 20.0, 29.0, 44.0, 52.0, 68.0, 76.0,...	[0.4090454254569629, 1.016575178648564, 3.2294...	0.13463	0.978949	CTL07C	4	6.471466
CTL07C_6	2.861219	0.030355	0.717828	0.424542	[0.7178284323935998, 1.3666883712911995, 2.714...	[0.0, 16.0, 24.0, 39.0, 48.0, 63.0]	[0.42454248274224105, 2.2135828308679812, 3.49...	0.030066	0.982106	CTL07C	6	3.285761
CTL08A_1	1.187035	0.033521	0.33419	0.103732	[0.33418952506655986, 1.1351766731587196, 3.25...	[0.0, 39.0, 48.0, 63.0, 72.0, 88.0, 96.0, 111.0]	[0.10373199917555276, 3.304242116545631, 4.849...	0.085182	0.980946	CTL08A	1	1.290767
CTL08A_2	0.706487	0.033213	0.165209	0.120179	[0.16520885806607996, 0.42682587784329584, 0.6...	[0.0, 15.0, 24.0, 39.0, 48.0, 63.0, 72.0, 87.0...	[0.12017926217257657, 0.5763851701267808, 0.98...	0.02542	0.996042	CTL08A	2	0.826666
CTL08A_3	4.495572	0.021725	0.369839	0.164502	[0.3698385596056799, 0.6810055432149598, 1.573...	[0.0, 5.0, 20.0, 29.0, 44.0, 52.0, 68.0, 76.0,...	[0.16450164389087973, 0.680346996777927, 2.610...	0.151265	0.973682	CTL08A	3	4.660074
CTL08A_5	30.191408	0.003436	0.718488	0.720853	[0.7184884989571197, 0.8260278491119677, 3.779...	[0.0, 16.0, 17.0, 24.0, 39.0, 48.0, 63.0]	[0.7208533279078502, 2.4271379428335926, 2.536...	0.073788	0.886176	CTL08A	5	30.912261
CTL09A_2	0.263507	0.036516	0.416052	0.326098	[0.41605228590047993, 0.8020691253345598, 1.64...	[33.0, 49.0, 57.0, 72.0, 81.0, 96.0, 105.0, 12...	[0.9418809126629182, 1.6397397810736654, 2.174...	0.041404	0.9842	CTL09A	2	0.589605
CTL09A_3	2.67779	0.028298	1.09468	0.4693	[1.0946797761170877, 2.2220952270454073, 3.557...	[15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0, 96....	[1.8852781353057484, 3.07269361924069, 5.86530...	0.0525	0.98176	CTL09A	3	3.14709
CTL09A_4	3.743787	0.024477	0.856375	0.856375	[0.8563747115980797, 1.4846659608893753, 2.637...	[9.0, 24.0, 32.0, 48.0, 56.0, 73.0, 81.0, 96.0...	[1.778987723662873, 3.849072862477047, 5.30617...	0.108845	0.990837	CTL09A	4	4.600161
CTL09A_5	0.645037	0.044788	0.999207	1.372094	[0.9992065878129598, 1.4917047366392635, 2.493...	[0.0, 8.0, 24.0, 32.0, 47.0, 56.0, 71.0]	[1.3720943628331366, 1.6500428832472247, 2.616...	0.013601	0.98726	CTL09A	5	2.017131
H1_1	0.881922	0.022767	0.127647	0.032898	[0.12764744386243193, 0.2877317192128319, 0.33...	[9.0, 24.0, 33.0, 48.0, 57.0, 72.0, 83.0, 96.0...	[0.2334544692034437, 0.6740965916339468, 1.020...	0.103301	0.98154	H1	1	0.91482
H1_2	4.602859	0.013332	2.472889	2.472889	[2.4728886058766393, 2.915316716446655, 3.1268...	[0.0, 15.0, 39.0, 47.0, 64.0, 72.0, 87.0, 95.0...	[2.472888605876677, 3.4918995137855164, 5.6118...	0.116448	0.957078	H1	2	7.075747
H9_1	4.27921	0.024254	0.377707	0.350742	[0.3777067706471999, 0.9652240400097598, 2.490...	[0.0, 15.0, 24.0, 40.0, 48.0, 63.0, 72.0, 87.0...	[0.35074196350559994, 2.2284424262323013, 3.73...	0.046817	0.986148	H9	1	4.629952
H9_2	0.659132	0.045415	0.301872	0.153647	[0.30187165062959986, 1.850863636851551, 3.155...	[15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0]	[0.7971585632554442, 1.4548830570166933, 3.368...	0.01872	0.999084	H9	2	0.812778
H9_3	11.484083	0.015581	0.90592	0.3021	[0.9059195979950396, 1.1298801829973755, 1.425...	[0.0, 5.0, 20.0, 29.0, 44.0, 52.0, 68.0, 76.0,...	[0.30210013520928314, 1.2325485628117843, 4.50...	0.189097	0.975495	H9	3	11.786183
H9_5	1.264116	0.023808	0.809685	0.753878	[0.8096849757622797, 0.9034534152302397, 1.793...	[0.0, 16.0, 17.0, 39.0, 48.0, 63.0]	[0.7538782216300566, 1.3399656458665576, 1.384...	0.01269	0.965619	H9	5	2.017994
KTD8.2_1	0.238791	0.041092	0.550485	0.550485	[0.5504846337575998, 0.9347023082408397, 1.524...	[0.0, 39.0, 48.0, 63.0, 72.0, 88.0, 96.0, 111.0]	[0.5504846337576019, 1.4975108560653476, 2.028...	0.018369	0.986486	KTD8.2	1	0.789276
KTD8.2_2	0.377419	0.039801	0.713858	1.75361	[0.7138583617075197, 1.1289241745020795, 3.124...	[0.0, 15.0, 24.0, 39.0, 48.0, 63.0, 72.0, 87.0...	[1.753609889235595, 2.06184030467382, 2.357191...	0.046724	0.987279	KTD8.2	2	2.131029
KTD8.2_3	2.067121	0.018607	0.107452	0.056472	[0.10745158306233597, 0.3914869295194559, 0.60...	[9.0, 28.0, 33.0, 48.0, 57.0, 72.0, 80.0, 96.0...	[0.43331846896985615, 1.4698020953022803, 1.80...	0.144407	0.988663	KTD8.2	3	2.123593
KTD8.2_4	1.688852	0.026211	1.417346	1.347096	[1.4173458607295994, 2.1666846135959994, 2.887...	[0.0, 16.0, 24.0, 39.0, 48.0, 63.0]	[1.3470964626644197, 2.227020170936482, 2.8263...	0.002315	0.987125	KTD8.2	4	3.035949
UCSFi001-A_2	0.588666	0.026581	0.470745	0.461125	[0.4707453288189598, 1.1102174528831996, 1.745...	[24.0, 33.0, 49.0, 57.0, 72.0, 81.0, 96.0, 105...	[0.9865636607443292, 1.2876735048588026, 2.037...	0.031031	0.970674	UCSFi001-A	2	1.049792
UCSFi001-A_3	1.067308	0.025661	0.823938	0.73609	[0.8239383636753597, 1.0375904860577996, 1.344...	[0.0, 15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0...	[0.7360902739853485, 1.2371900959914608, 1.644...	0.007454	0.995604	UCSFi001-A	3	1.803399
UCSFi001-A_4	11.891799	0.016863	0.65714	0.65714	[0.6571397848564797, 1.3643807979277436, 3.360...	[0.0, 8.0, 25.0, 33.0, 48.0, 56.0, 73.0, 81.0,...	[0.6571397848564793, 2.374656891528188, 6.8928...	0.053775	0.99402	UCSFi001-A	4	12.548939
UCSFi001-A_5	0.695858	0.055867	1.776417	1.328369	[1.7764168326609595, 2.3372079343318073, 3.079...	[0.0, 16.0, 24.0, 39.0, 48.0, 63.0]	[1.3283694521265805, 2.333591404662628, 3.2921...	0.02179	0.981117	UCSFi001-A	5	2.024228

fitted_df[fitted_df['a+c'] < 0].shape

(0, 12)

fitted_df_filtered = fitted_df[fitted_df['r2'] > 0.9]
fitted_df_filtered

	a	rate	min(y)	c	mean_cum	split_time	y_fitted	MSLE	r2	Line	split	a+c
CTL01A_2	0.140845	0.031439	0.128738	0.051989	[0.12873836706191996, 0.5126940096263999, 0.75...	[49.0, 57.0, 72.0, 81.0, 96.0, 105.0, 120.0]	[0.5684601783697514, 0.7564306877808943, 1.265...	0.033141	0.955038	CTL01A	2	0.192835
CTL01A_4	6.709435	0.020925	1.071547	0.93823	[1.0715473444571997, 1.7103960320254554, 3.865...	[0.0, 8.0, 25.0, 33.0, 48.0, 56.0, 73.0]	[0.9382302189532821, 2.1608528979695825, 5.549...	0.024887	0.958803	CTL01A	4	7.647665
CTL02A_1	1.358287	0.02225	1.065226	0.550477	[1.0652259377527198, 1.4048785412085596, 2.313...	[39.0, 48.0, 63.0, 72.0, 88.0, 96.0, 111.0, 12...	[2.4269662693898706, 3.144128958826294, 4.7098...	0.10339	0.974893	CTL02A	1	1.908765
CTL02A_2	0.954612	0.043378	1.26411	0.76608	[1.2641101587982075, 1.7939214715189675, 4.596...	[15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0, 96.0]	[1.6412790277239497, 2.5151392692655543, 4.993...	0.016467	0.992677	CTL02A	2	1.720692
CTL02A_3	16.613953	0.016347	1.649741	0.656578	[1.6497408713817594, 2.607119548807967, 3.9639...	[0.0, 5.0, 20.0, 29.0, 44.0, 52.0, 68.0, 76.0,...	[0.6565776402558363, 2.0715333393022206, 7.081...	0.11749	0.975446	CTL02A	3	17.27053
CTL02A_5	0.682361	0.037966	0.654197	0.588409	[0.6541966858658399, 0.9161832703838398, 1.754...	[0.0, 16.0, 24.0, 39.0, 48.0, 63.0]	[0.5884094472451199, 1.1586862058833431, 1.603...	0.007286	0.983085	CTL02A	5	1.27077
CTL04E_2	0.821185	0.024744	0.299609	0.299609	[0.2996085652689599, 1.1036059070299196, 1.703...	[24.0, 33.0, 49.0, 57.0, 72.0, 81.0, 96.0, 105...	[0.9655562584883766, 1.3365081793448954, 2.239...	0.028769	0.985605	CTL04E	2	1.120794
CTL04E_3	1.306325	0.023063	2.123347	2.123347	[2.1233470930991993, 2.4315673509784794, 2.677...	[15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0, 96....	[2.6632786987130626, 3.089169790618284, 4.0282...	0.068529	0.976291	CTL04E	3	3.429672
CTL04E_4	9.612778	0.017852	1.218989	0.859733	[1.2189894108551995, 2.1238454675329193, 2.880...	[0.0, 8.0, 25.0, 33.0, 48.0, 56.0, 73.0, 81.0,...	[0.8597330722454402, 2.3354356000019507, 6.266...	0.044278	0.990038	CTL04E	4	10.472511
CTL05A_1	0.831961	0.030813	0.779193	0.497694	[0.7791926205821758, 2.426386553802719, 4.5256...	[39.0, 48.0, 63.0, 72.0, 88.0, 96.0, 111.0, 12...	[2.432703578982128, 3.3169982277731034, 5.4623...	0.052295	0.99813	CTL05A	1	1.329655
CTL05A_2	0.055631	0.043012	0.205236	0.491117	[0.20523627369755992, 0.5079725389905838, 0.63...	[9.0, 24.0, 33.0, 48.0, 59.0, 72.0, 81.0, 96.0...	[0.5174145386527128, 0.5916687051661024, 0.665...	0.00577	0.999672	CTL05A	2	0.546748
CTL05A_3	2.543079	0.01896	1.430206	0.870664	[1.4302055733008394, 1.6829849546056073, 1.766...	[0.0, 15.0, 23.0, 39.0, 47.0, 64.0, 72.0, 87.0...	[0.8706640646764798, 1.7072362370661094, 2.260...	0.079341	0.984739	CTL05A	3	3.413743
CTL06F_1	0.192261	0.038794	0.186632	0.149139	[0.18663200746559994, 0.5037948979217999, 0.99...	[0.0, 39.0, 48.0, 63.0, 72.0, 88.0, 96.0, 111....	[0.14913877596194025, 0.8297829559442185, 1.19...	0.008407	0.998507	CTL06F	1	0.3414
CTL06F_2	0.178955	0.048632	0.221248	0.603675	[0.22124802574367994, 0.5315105005565759, 0.98...	[0.0, 9.0, 24.0, 33.0, 48.0, 59.0, 72.0, 81.0,...	[0.6036745082056189, 0.701943955589503, 0.9996...	0.014467	0.998732	CTL06F	2	0.78263
CTL06F_3	9.101519	0.017721	0.835248	0.584532	[0.8352482294782076, 1.4114732831694714, 2.609...	[0.0, 5.0, 20.0, 29.0, 44.0, 52.0, 68.0, 76.0,...	[0.5845324628693316, 1.4277887166726817, 4.455...	0.035992	0.9908	CTL06F	3	9.686051
CTL06F_5	1.517014	0.028446	0.995236	1.080533	[0.9952359126703195, 2.065253135791535, 2.6851...	[0.0, 16.0, 24.0, 39.0, 48.0, 63.0]	[1.0805325124857454, 1.9549269947108237, 2.566...	0.001386	0.996178	CTL06F	5	2.597547
CTL07C_2	0.247166	0.031126	0.098445	0.039209	[0.09844493853571196, 0.27541168560691187, 0.4...	[9.0, 24.0, 33.0, 49.0, 57.0, 72.0, 81.0, 96.0...	[0.11911823217794204, 0.31373406561857875, 0.4...	0.004426	0.990575	CTL07C	2	0.286375
CTL07C_3	1.613569	0.035564	2.400426	2.061275	[2.400426353463839, 3.2856292908866864, 4.3438...	[0.0, 15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0]	[2.0612745335144926, 3.198564283424051, 4.2362...	0.003228	0.998319	CTL07C	3	3.674844
CTL07C_4	6.062421	0.019101	0.478994	0.409045	[0.47899434749327985, 0.8008914021730558, 1.50...	[0.0, 5.0, 20.0, 29.0, 44.0, 52.0, 68.0, 76.0,...	[0.4090454254569629, 1.016575178648564, 3.2294...	0.13463	0.978949	CTL07C	4	6.471466
CTL07C_6	2.861219	0.030355	0.717828	0.424542	[0.7178284323935998, 1.3666883712911995, 2.714...	[0.0, 16.0, 24.0, 39.0, 48.0, 63.0]	[0.42454248274224105, 2.2135828308679812, 3.49...	0.030066	0.982106	CTL07C	6	3.285761
CTL08A_1	1.187035	0.033521	0.33419	0.103732	[0.33418952506655986, 1.1351766731587196, 3.25...	[0.0, 39.0, 48.0, 63.0, 72.0, 88.0, 96.0, 111.0]	[0.10373199917555276, 3.304242116545631, 4.849...	0.085182	0.980946	CTL08A	1	1.290767
CTL08A_2	0.706487	0.033213	0.165209	0.120179	[0.16520885806607996, 0.42682587784329584, 0.6...	[0.0, 15.0, 24.0, 39.0, 48.0, 63.0, 72.0, 87.0...	[0.12017926217257657, 0.5763851701267808, 0.98...	0.02542	0.996042	CTL08A	2	0.826666
CTL08A_3	4.495572	0.021725	0.369839	0.164502	[0.3698385596056799, 0.6810055432149598, 1.573...	[0.0, 5.0, 20.0, 29.0, 44.0, 52.0, 68.0, 76.0,...	[0.16450164389087973, 0.680346996777927, 2.610...	0.151265	0.973682	CTL08A	3	4.660074
CTL09A_2	0.263507	0.036516	0.416052	0.326098	[0.41605228590047993, 0.8020691253345598, 1.64...	[33.0, 49.0, 57.0, 72.0, 81.0, 96.0, 105.0, 12...	[0.9418809126629182, 1.6397397810736654, 2.174...	0.041404	0.9842	CTL09A	2	0.589605
CTL09A_3	2.67779	0.028298	1.09468	0.4693	[1.0946797761170877, 2.2220952270454073, 3.557...	[15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0, 96....	[1.8852781353057484, 3.07269361924069, 5.86530...	0.0525	0.98176	CTL09A	3	3.14709
CTL09A_4	3.743787	0.024477	0.856375	0.856375	[0.8563747115980797, 1.4846659608893753, 2.637...	[9.0, 24.0, 32.0, 48.0, 56.0, 73.0, 81.0, 96.0...	[1.778987723662873, 3.849072862477047, 5.30617...	0.108845	0.990837	CTL09A	4	4.600161
CTL09A_5	0.645037	0.044788	0.999207	1.372094	[0.9992065878129598, 1.4917047366392635, 2.493...	[0.0, 8.0, 24.0, 32.0, 47.0, 56.0, 71.0]	[1.3720943628331366, 1.6500428832472247, 2.616...	0.013601	0.98726	CTL09A	5	2.017131
H1_1	0.881922	0.022767	0.127647	0.032898	[0.12764744386243193, 0.2877317192128319, 0.33...	[9.0, 24.0, 33.0, 48.0, 57.0, 72.0, 83.0, 96.0...	[0.2334544692034437, 0.6740965916339468, 1.020...	0.103301	0.98154	H1	1	0.91482
H1_2	4.602859	0.013332	2.472889	2.472889	[2.4728886058766393, 2.915316716446655, 3.1268...	[0.0, 15.0, 39.0, 47.0, 64.0, 72.0, 87.0, 95.0...	[2.472888605876677, 3.4918995137855164, 5.6118...	0.116448	0.957078	H1	2	7.075747
H9_1	4.27921	0.024254	0.377707	0.350742	[0.3777067706471999, 0.9652240400097598, 2.490...	[0.0, 15.0, 24.0, 40.0, 48.0, 63.0, 72.0, 87.0...	[0.35074196350559994, 2.2284424262323013, 3.73...	0.046817	0.986148	H9	1	4.629952
H9_2	0.659132	0.045415	0.301872	0.153647	[0.30187165062959986, 1.850863636851551, 3.155...	[15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0]	[0.7971585632554442, 1.4548830570166933, 3.368...	0.01872	0.999084	H9	2	0.812778
H9_3	11.484083	0.015581	0.90592	0.3021	[0.9059195979950396, 1.1298801829973755, 1.425...	[0.0, 5.0, 20.0, 29.0, 44.0, 52.0, 68.0, 76.0,...	[0.30210013520928314, 1.2325485628117843, 4.50...	0.189097	0.975495	H9	3	11.786183
H9_5	1.264116	0.023808	0.809685	0.753878	[0.8096849757622797, 0.9034534152302397, 1.793...	[0.0, 16.0, 17.0, 39.0, 48.0, 63.0]	[0.7538782216300566, 1.3399656458665576, 1.384...	0.01269	0.965619	H9	5	2.017994
KTD8.2_1	0.238791	0.041092	0.550485	0.550485	[0.5504846337575998, 0.9347023082408397, 1.524...	[0.0, 39.0, 48.0, 63.0, 72.0, 88.0, 96.0, 111.0]	[0.5504846337576019, 1.4975108560653476, 2.028...	0.018369	0.986486	KTD8.2	1	0.789276
KTD8.2_2	0.377419	0.039801	0.713858	1.75361	[0.7138583617075197, 1.1289241745020795, 3.124...	[0.0, 15.0, 24.0, 39.0, 48.0, 63.0, 72.0, 87.0...	[1.753609889235595, 2.06184030467382, 2.357191...	0.046724	0.987279	KTD8.2	2	2.131029
KTD8.2_3	2.067121	0.018607	0.107452	0.056472	[0.10745158306233597, 0.3914869295194559, 0.60...	[9.0, 28.0, 33.0, 48.0, 57.0, 72.0, 80.0, 96.0...	[0.43331846896985615, 1.4698020953022803, 1.80...	0.144407	0.988663	KTD8.2	3	2.123593
KTD8.2_4	1.688852	0.026211	1.417346	1.347096	[1.4173458607295994, 2.1666846135959994, 2.887...	[0.0, 16.0, 24.0, 39.0, 48.0, 63.0]	[1.3470964626644197, 2.227020170936482, 2.8263...	0.002315	0.987125	KTD8.2	4	3.035949
UCSFi001-A_2	0.588666	0.026581	0.470745	0.461125	[0.4707453288189598, 1.1102174528831996, 1.745...	[24.0, 33.0, 49.0, 57.0, 72.0, 81.0, 96.0, 105...	[0.9865636607443292, 1.2876735048588026, 2.037...	0.031031	0.970674	UCSFi001-A	2	1.049792
UCSFi001-A_3	1.067308	0.025661	0.823938	0.73609	[0.8239383636753597, 1.0375904860577996, 1.344...	[0.0, 15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0...	[0.7360902739853485, 1.2371900959914608, 1.644...	0.007454	0.995604	UCSFi001-A	3	1.803399
UCSFi001-A_4	11.891799	0.016863	0.65714	0.65714	[0.6571397848564797, 1.3643807979277436, 3.360...	[0.0, 8.0, 25.0, 33.0, 48.0, 56.0, 73.0, 81.0,...	[0.6571397848564793, 2.374656891528188, 6.8928...	0.053775	0.99402	UCSFi001-A	4	12.548939
UCSFi001-A_5	0.695858	0.055867	1.776417	1.328369	[1.7764168326609595, 2.3372079343318073, 3.079...	[0.0, 16.0, 24.0, 39.0, 48.0, 63.0]	[1.3283694521265805, 2.333591404662628, 3.2921...	0.02179	0.981117	UCSFi001-A	5	2.024228

fig, ax = plt.subplots()
sns.barplot(data = fitted_df_filtered, x = 'split', y = 'rate', order = ['1', '2', '3', '4', '5', '6'], ax = ax)#, hue = 'Line', palette=line_palette)
_ = ax.set_ylabel('Growth rate', fontsize = 20)
_ = ax.set_yticklabels(ax.get_yticklabels(), fontsize = 15)
_ = ax.set_xlabel('Passage', fontsize = 20)
_ = ax.set_xticklabels(ax.get_xticklabels(), fontsize = 15)

fig, ax = plt.subplots(figsize = (10,4))
fitted_df_filtered['split'] = fitted_df_filtered['split'].astype('int')
fitted_df_filtered['rate'] = fitted_df_filtered['rate'].astype('float64')
sns.lineplot(data = fitted_df_filtered, x = 'split', y = 'rate', hue = 'Line',
              ax = ax, palette=line_palette)
_ = ax.set_ylabel('Growth rate', fontsize = 20)
_ = ax.set_yticklabels(ax.get_yticklabels(), fontsize = 15)
_ = ax.set_xlabel('Passage', fontsize = 20)
_ = ax.set_xticklabels(ax.get_xticklabels(), fontsize = 15)
ax.legend(bbox_to_anchor = (1,1))

<matplotlib.legend.Legend at 0x7fe48429deb0>

fig, ax = plt.subplots()
sns.boxplot(data = fitted_df_filtered, x = 'Line', y = 'rate', ax = ax, palette=line_palette)
_ = ax.set_ylabel('Rate of area growth', fontsize = 20)
_ = ax.set_yticklabels(ax.get_yticklabels(), fontsize = 15)
_ = ax.set_xlabel('Passage', fontsize = 20)
_ = ax.set_xticklabels(ax.get_xticklabels(), fontsize = 15, rotation = 90)

fitted_df_filtered.sort_values(by = 'rate').to_csv('../../data/csv/iPSC_fitted_exp_area_sum_per_split.csv')

fitted_df_filtered.sort_values(by = 'rate')

	a	rate	min(y)	c	mean_cum	split_time	y_fitted	MSLE	r2	Line	split	a+c
H1_2	4.602859	0.013332	2.472889	2.472889	[2.4728886058766393, 2.915316716446655, 3.1268...	[0.0, 15.0, 39.0, 47.0, 64.0, 72.0, 87.0, 95.0...	[2.472888605876677, 3.4918995137855164, 5.6118...	0.116448	0.957078	H1	2	7.075747
H9_3	11.484083	0.015581	0.90592	0.3021	[0.9059195979950396, 1.1298801829973755, 1.425...	[0.0, 5.0, 20.0, 29.0, 44.0, 52.0, 68.0, 76.0,...	[0.30210013520928314, 1.2325485628117843, 4.50...	0.189097	0.975495	H9	3	11.786183
CTL02A_3	16.613953	0.016347	1.649741	0.656578	[1.6497408713817594, 2.607119548807967, 3.9639...	[0.0, 5.0, 20.0, 29.0, 44.0, 52.0, 68.0, 76.0,...	[0.6565776402558363, 2.0715333393022206, 7.081...	0.11749	0.975446	CTL02A	3	17.27053
UCSFi001-A_4	11.891799	0.016863	0.65714	0.65714	[0.6571397848564797, 1.3643807979277436, 3.360...	[0.0, 8.0, 25.0, 33.0, 48.0, 56.0, 73.0, 81.0,...	[0.6571397848564793, 2.374656891528188, 6.8928...	0.053775	0.99402	UCSFi001-A	4	12.548939
CTL06F_3	9.101519	0.017721	0.835248	0.584532	[0.8352482294782076, 1.4114732831694714, 2.609...	[0.0, 5.0, 20.0, 29.0, 44.0, 52.0, 68.0, 76.0,...	[0.5845324628693316, 1.4277887166726817, 4.455...	0.035992	0.9908	CTL06F	3	9.686051
CTL04E_4	9.612778	0.017852	1.218989	0.859733	[1.2189894108551995, 2.1238454675329193, 2.880...	[0.0, 8.0, 25.0, 33.0, 48.0, 56.0, 73.0, 81.0,...	[0.8597330722454402, 2.3354356000019507, 6.266...	0.044278	0.990038	CTL04E	4	10.472511
KTD8.2_3	2.067121	0.018607	0.107452	0.056472	[0.10745158306233597, 0.3914869295194559, 0.60...	[9.0, 28.0, 33.0, 48.0, 57.0, 72.0, 80.0, 96.0...	[0.43331846896985615, 1.4698020953022803, 1.80...	0.144407	0.988663	KTD8.2	3	2.123593
CTL05A_3	2.543079	0.018960	1.430206	0.870664	[1.4302055733008394, 1.6829849546056073, 1.766...	[0.0, 15.0, 23.0, 39.0, 47.0, 64.0, 72.0, 87.0...	[0.8706640646764798, 1.7072362370661094, 2.260...	0.079341	0.984739	CTL05A	3	3.413743
CTL07C_4	6.062421	0.019101	0.478994	0.409045	[0.47899434749327985, 0.8008914021730558, 1.50...	[0.0, 5.0, 20.0, 29.0, 44.0, 52.0, 68.0, 76.0,...	[0.4090454254569629, 1.016575178648564, 3.2294...	0.13463	0.978949	CTL07C	4	6.471466
CTL01A_4	6.709435	0.020925	1.071547	0.93823	[1.0715473444571997, 1.7103960320254554, 3.865...	[0.0, 8.0, 25.0, 33.0, 48.0, 56.0, 73.0]	[0.9382302189532821, 2.1608528979695825, 5.549...	0.024887	0.958803	CTL01A	4	7.647665
CTL08A_3	4.495572	0.021725	0.369839	0.164502	[0.3698385596056799, 0.6810055432149598, 1.573...	[0.0, 5.0, 20.0, 29.0, 44.0, 52.0, 68.0, 76.0,...	[0.16450164389087973, 0.680346996777927, 2.610...	0.151265	0.973682	CTL08A	3	4.660074
CTL02A_1	1.358287	0.022250	1.065226	0.550477	[1.0652259377527198, 1.4048785412085596, 2.313...	[39.0, 48.0, 63.0, 72.0, 88.0, 96.0, 111.0, 12...	[2.4269662693898706, 3.144128958826294, 4.7098...	0.10339	0.974893	CTL02A	1	1.908765
H1_1	0.881922	0.022767	0.127647	0.032898	[0.12764744386243193, 0.2877317192128319, 0.33...	[9.0, 24.0, 33.0, 48.0, 57.0, 72.0, 83.0, 96.0...	[0.2334544692034437, 0.6740965916339468, 1.020...	0.103301	0.98154	H1	1	0.91482
CTL04E_3	1.306325	0.023063	2.123347	2.123347	[2.1233470930991993, 2.4315673509784794, 2.677...	[15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0, 96....	[2.6632786987130626, 3.089169790618284, 4.0282...	0.068529	0.976291	CTL04E	3	3.429672
H9_5	1.264116	0.023808	0.809685	0.753878	[0.8096849757622797, 0.9034534152302397, 1.793...	[0.0, 16.0, 17.0, 39.0, 48.0, 63.0]	[0.7538782216300566, 1.3399656458665576, 1.384...	0.01269	0.965619	H9	5	2.017994
H9_1	4.27921	0.024254	0.377707	0.350742	[0.3777067706471999, 0.9652240400097598, 2.490...	[0.0, 15.0, 24.0, 40.0, 48.0, 63.0, 72.0, 87.0...	[0.35074196350559994, 2.2284424262323013, 3.73...	0.046817	0.986148	H9	1	4.629952
CTL09A_4	3.743787	0.024477	0.856375	0.856375	[0.8563747115980797, 1.4846659608893753, 2.637...	[9.0, 24.0, 32.0, 48.0, 56.0, 73.0, 81.0, 96.0...	[1.778987723662873, 3.849072862477047, 5.30617...	0.108845	0.990837	CTL09A	4	4.600161
CTL04E_2	0.821185	0.024744	0.299609	0.299609	[0.2996085652689599, 1.1036059070299196, 1.703...	[24.0, 33.0, 49.0, 57.0, 72.0, 81.0, 96.0, 105...	[0.9655562584883766, 1.3365081793448954, 2.239...	0.028769	0.985605	CTL04E	2	1.120794
UCSFi001-A_3	1.067308	0.025661	0.823938	0.73609	[0.8239383636753597, 1.0375904860577996, 1.344...	[0.0, 15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0...	[0.7360902739853485, 1.2371900959914608, 1.644...	0.007454	0.995604	UCSFi001-A	3	1.803399
KTD8.2_4	1.688852	0.026211	1.417346	1.347096	[1.4173458607295994, 2.1666846135959994, 2.887...	[0.0, 16.0, 24.0, 39.0, 48.0, 63.0]	[1.3470964626644197, 2.227020170936482, 2.8263...	0.002315	0.987125	KTD8.2	4	3.035949
UCSFi001-A_2	0.588666	0.026581	0.470745	0.461125	[0.4707453288189598, 1.1102174528831996, 1.745...	[24.0, 33.0, 49.0, 57.0, 72.0, 81.0, 96.0, 105...	[0.9865636607443292, 1.2876735048588026, 2.037...	0.031031	0.970674	UCSFi001-A	2	1.049792
CTL09A_3	2.67779	0.028298	1.09468	0.4693	[1.0946797761170877, 2.2220952270454073, 3.557...	[15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0, 96....	[1.8852781353057484, 3.07269361924069, 5.86530...	0.0525	0.98176	CTL09A	3	3.14709
CTL06F_5	1.517014	0.028446	0.995236	1.080533	[0.9952359126703195, 2.065253135791535, 2.6851...	[0.0, 16.0, 24.0, 39.0, 48.0, 63.0]	[1.0805325124857454, 1.9549269947108237, 2.566...	0.001386	0.996178	CTL06F	5	2.597547
CTL07C_6	2.861219	0.030355	0.717828	0.424542	[0.7178284323935998, 1.3666883712911995, 2.714...	[0.0, 16.0, 24.0, 39.0, 48.0, 63.0]	[0.42454248274224105, 2.2135828308679812, 3.49...	0.030066	0.982106	CTL07C	6	3.285761
CTL05A_1	0.831961	0.030813	0.779193	0.497694	[0.7791926205821758, 2.426386553802719, 4.5256...	[39.0, 48.0, 63.0, 72.0, 88.0, 96.0, 111.0, 12...	[2.432703578982128, 3.3169982277731034, 5.4623...	0.052295	0.99813	CTL05A	1	1.329655
CTL07C_2	0.247166	0.031126	0.098445	0.039209	[0.09844493853571196, 0.27541168560691187, 0.4...	[9.0, 24.0, 33.0, 49.0, 57.0, 72.0, 81.0, 96.0...	[0.11911823217794204, 0.31373406561857875, 0.4...	0.004426	0.990575	CTL07C	2	0.286375
CTL01A_2	0.140845	0.031439	0.128738	0.051989	[0.12873836706191996, 0.5126940096263999, 0.75...	[49.0, 57.0, 72.0, 81.0, 96.0, 105.0, 120.0]	[0.5684601783697514, 0.7564306877808943, 1.265...	0.033141	0.955038	CTL01A	2	0.192835
CTL08A_2	0.706487	0.033213	0.165209	0.120179	[0.16520885806607996, 0.42682587784329584, 0.6...	[0.0, 15.0, 24.0, 39.0, 48.0, 63.0, 72.0, 87.0...	[0.12017926217257657, 0.5763851701267808, 0.98...	0.02542	0.996042	CTL08A	2	0.826666
CTL08A_1	1.187035	0.033521	0.33419	0.103732	[0.33418952506655986, 1.1351766731587196, 3.25...	[0.0, 39.0, 48.0, 63.0, 72.0, 88.0, 96.0, 111.0]	[0.10373199917555276, 3.304242116545631, 4.849...	0.085182	0.980946	CTL08A	1	1.290767
CTL07C_3	1.613569	0.035564	2.400426	2.061275	[2.400426353463839, 3.2856292908866864, 4.3438...	[0.0, 15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0]	[2.0612745335144926, 3.198564283424051, 4.2362...	0.003228	0.998319	CTL07C	3	3.674844
CTL09A_2	0.263507	0.036516	0.416052	0.326098	[0.41605228590047993, 0.8020691253345598, 1.64...	[33.0, 49.0, 57.0, 72.0, 81.0, 96.0, 105.0, 12...	[0.9418809126629182, 1.6397397810736654, 2.174...	0.041404	0.9842	CTL09A	2	0.589605
CTL02A_5	0.682361	0.037966	0.654197	0.588409	[0.6541966858658399, 0.9161832703838398, 1.754...	[0.0, 16.0, 24.0, 39.0, 48.0, 63.0]	[0.5884094472451199, 1.1586862058833431, 1.603...	0.007286	0.983085	CTL02A	5	1.27077
CTL06F_1	0.192261	0.038794	0.186632	0.149139	[0.18663200746559994, 0.5037948979217999, 0.99...	[0.0, 39.0, 48.0, 63.0, 72.0, 88.0, 96.0, 111....	[0.14913877596194025, 0.8297829559442185, 1.19...	0.008407	0.998507	CTL06F	1	0.3414
KTD8.2_2	0.377419	0.039801	0.713858	1.75361	[0.7138583617075197, 1.1289241745020795, 3.124...	[0.0, 15.0, 24.0, 39.0, 48.0, 63.0, 72.0, 87.0...	[1.753609889235595, 2.06184030467382, 2.357191...	0.046724	0.987279	KTD8.2	2	2.131029
KTD8.2_1	0.238791	0.041092	0.550485	0.550485	[0.5504846337575998, 0.9347023082408397, 1.524...	[0.0, 39.0, 48.0, 63.0, 72.0, 88.0, 96.0, 111.0]	[0.5504846337576019, 1.4975108560653476, 2.028...	0.018369	0.986486	KTD8.2	1	0.789276
CTL05A_2	0.055631	0.043012	0.205236	0.491117	[0.20523627369755992, 0.5079725389905838, 0.63...	[9.0, 24.0, 33.0, 48.0, 59.0, 72.0, 81.0, 96.0...	[0.5174145386527128, 0.5916687051661024, 0.665...	0.00577	0.999672	CTL05A	2	0.546748
CTL02A_2	0.954612	0.043378	1.26411	0.76608	[1.2641101587982075, 1.7939214715189675, 4.596...	[15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0, 96.0]	[1.6412790277239497, 2.5151392692655543, 4.993...	0.016467	0.992677	CTL02A	2	1.720692
CTL09A_5	0.645037	0.044788	0.999207	1.372094	[0.9992065878129598, 1.4917047366392635, 2.493...	[0.0, 8.0, 24.0, 32.0, 47.0, 56.0, 71.0]	[1.3720943628331366, 1.6500428832472247, 2.616...	0.013601	0.98726	CTL09A	5	2.017131
H9_2	0.659132	0.045415	0.301872	0.153647	[0.30187165062959986, 1.850863636851551, 3.155...	[15.0, 24.0, 39.0, 50.0, 63.0, 72.0, 87.0]	[0.7971585632554442, 1.4548830570166933, 3.368...	0.01872	0.999084	H9	2	0.812778
CTL06F_2	0.178955	0.048632	0.221248	0.603675	[0.22124802574367994, 0.5315105005565759, 0.98...	[0.0, 9.0, 24.0, 33.0, 48.0, 59.0, 72.0, 81.0,...	[0.6036745082056189, 0.701943955589503, 0.9996...	0.014467	0.998732	CTL06F	2	0.78263
UCSFi001-A_5	0.695858	0.055867	1.776417	1.328369	[1.7764168326609595, 2.3372079343318073, 3.079...	[0.0, 16.0, 24.0, 39.0, 48.0, 63.0]	[1.3283694521265805, 2.333591404662628, 3.2921...	0.02179	0.981117	UCSFi001-A	5	2.024228

fitted_df['split'] = fitted_df['split'].astype('int')
fitted_df['rate'] = fitted_df['rate'].astype('float64')

pd.DataFrame(fitted_df.groupby('Line')['rate'].mean().sort_values())

	rate
Line
H1	0.018050
CTL08A	0.022974
CTL04E	0.025820
CTL01A	0.026182
H9	0.027264
CTL07C	0.029036
CTL02A	0.029985
CTL05A	0.030928
UCSFi001-A	0.031243
KTD8.2	0.031428
CTL06F	0.033399
CTL09A	0.033520

data_tot = []

for line_n in fitted_df.index:
    sub = fitted_df.loc[line_n]
    data = pd.DataFrame({'mean_cum': sub['mean_cum'], 'split_time': sub['split_time'], 'line_n': [line_n] * len(sub['mean_cum'])})
    data_tot.append(data)

data_tot = pd.concat(data_tot)

data_tot['Line'] = data_tot['line_n'].apply(lambda x: x.split('_')[0]).values
data_tot['split'] = data_tot['line_n'].apply(lambda x: x.split('_')[1]).values

fig, ax = plt.subplots(4,3, figsize = (20, 20))
ax = ax.flatten().T
ax_index = 0
fitted_param_line = {}

for line in order:

    fitted_param_line[line] = {}
    sub = data_tot[data_tot.Line == line]
    sub = sub.sort_values('split_time')
    
    if len(sub.split_time.unique()) > 5:
        # Calculate the cumulative sum of the mean total area for each split_time
        y = sub['mean_cum'].cumsum().values
        x = np.array(sub.split_time)

        try:
            popt, pcov = curve_fit(exp_model, x, y, p0=(max(y), 0.1, 0))

            fitted_param_line[line]['intercept'] = popt[0]
            fitted_param_line[line]['rate'] = popt[1]
            fitted_param_line[line]['mean_cum'] = y
            fitted_param_line[line]['split_time'] = x
            
            a, b, c = popt
            
            # Generate fitted y values
            y_fitted = exp_model(x, a, b, c)

            fitted_param_line[line]['y_fitted'] = y_fitted
            #fitted_param_line[line]['MSLE'] = mean_squared_log_error(y, y_fitted)
            fitted_param_line[line]['r2'] = r2_score(y, y_fitted)
            
            sns.lineplot(y = y_fitted, x = x, ax = ax[ax_index], markers = True)
            sns.scatterplot(y = y, x = x, ax = ax[ax_index], markers = True)
            ax[ax_index].xaxis.set_tick_params(rotation=90)
            ax[ax_index].set_title(f'{line}', fontsize = 30)
            ax[ax_index].set_ylabel('Increase in area ', fontsize = 20)
            ax[ax_index].set_xlabel('Time point', fontsize = 20)
            _ = ax[ax_index].set_xticklabels(ax[ax_index].get_xticklabels(), fontsize = 15)
            _ = ax[ax_index].set_yticklabels(ax[ax_index].get_yticklabels(), fontsize = 15)
            ax_index += 1
        
        except RuntimeError as e:
            print(f"Fitting failed for line_n {line_n}: {e}")
            
plt.tight_layout()

Fitting failed for line_n UCSFi001-A_5: Optimal parameters not found: Number of calls to function has reached maxfev = 800.

fitted_df_line = pd.DataFrame.from_dict(fitted_param_line).T
fitted_df_line = fitted_df_line[~fitted_df_line.intercept.isna()]
fitted_df_line.sort_values('rate')

	intercept	rate	mean_cum	split_time	y_fitted	r2
CTL04E	204.245148	0.009307	[1.2189894108551995, 2.8758556161662385, 4.999...	[0.0, 0.0, 8.0, 15.0, 16.0, 24.0, 24.0, 24.0, ...	[-35.001497262974425, -35.001497262974425, -19...	0.977045
KTD8.2	82.65117	0.010281	[0.5504846337575998, 1.9678304944871994, 2.681...	[0.0, 0.0, 0.0, 9.0, 15.0, 16.0, 24.0, 24.0, 2...	[-15.476692162327979, -15.476692162327979, -15...	0.98984
H9	110.894548	0.013802	[0.3777067706471999, 1.1873917464094796, 2.093...	[0.0, 0.0, 0.0, 5.0, 15.0, 15.0, 16.0, 17.0, 2...	[-37.324349401025074, -37.324349401025074, -37...	0.986461
UCSFi001-A	102.618779	0.013856	[0.8239383636753597, 1.4810781485318394, 3.257...	[0.0, 0.0, 0.0, 8.0, 15.0, 16.0, 24.0, 24.0, 2...	[-28.756872674622286, -28.756872674622286, -28...	0.975132
CTL07C	62.000942	0.015562	[0.7178284323935998, 1.1968227798868796, 3.597...	[0.0, 0.0, 0.0, 5.0, 9.0, 15.0, 16.0, 20.0, 24...	[-9.858067505526257, -9.858067505526257, -9.85...	0.996057
CTL05A	33.125403	0.017384	[1.4302055733008394, 1.6354418469983993, 3.318...	[0.0, 9.0, 15.0, 23.0, 24.0, 33.0, 39.0, 39.0,...	[-33.80482906977792, -28.194803471203237, -23....	0.95798
CTL02A	69.758992	0.018447	[1.6497408713817594, 2.3039375572475995, 4.911...	[0.0, 0.0, 5.0, 15.0, 16.0, 20.0, 24.0, 24.0, ...	[-36.696433146177405, -36.696433146177405, -29...	0.990371
CTL09A	51.576489	0.019058	[0.9992065878129598, 2.4909113244522234, 3.347...	[0.0, 8.0, 9.0, 15.0, 24.0, 24.0, 24.0, 32.0, ...	[-29.09169724724024, -20.597230803579677, -19....	0.990286
H1	13.460639	0.019555	[2.4728886058766393, 2.600536049739071, 5.5158...	[0.0, 9.0, 15.0, 24.0, 33.0, 39.0, 47.0, 48.0,...	[-10.695057299386022, -8.104773073130806, -6.1...	0.987598
CTL08A	39.333914	0.019842	[0.33418952506655986, 1.0526780240236797, 1.21...	[0.0, 0.0, 0.0, 0.0, 5.0, 15.0, 16.0, 17.0, 20...	[-21.429730367136756, -21.429730367136756, -21...	0.984026
CTL06F	37.338291	0.019961	[0.18663200746559994, 1.1818679201359195, 1.40...	[0.0, 0.0, 0.0, 0.0, 5.0, 9.0, 16.0, 20.0, 24....	[-16.228638125874095, -16.228638125874095, -16...	0.993179

Cumulative sum of the discrete derivative of the curves - per line per split

We use the logarithm of the area and then sum all the FOV for a specific time points in each line at each split. Then we smoothed it with gaussian_filter1d and computed the diff, corresponding to the first discrete derivative. We then use the cumsum() function to obtain the cumulative sum over the discrete differential of the growth.

fig, ax = plt.subplots(10,5, figsize = (5*10, 7*9), gridspec_kw={'hspace': 0.7})
ax = ax.flatten().T
ax_index = 0

for l in total_df.line.unique():
    
    #color = color_dict[l]

    sub = total_df[total_df.line == l]
    sub = sub.sort_values(by = 'datetime')
    sub = sub[sub.n_split != 'day']

    for split in sub.n_split.unique():

        subsub = sub[sub.n_split == split]

        
        # user defined function,
        # with `area_sum` return the sum of the areas of all the field of view captured for that line at that time point
        summary_df = preprocess(subsub, original_v='Area (microm2)', final_output='mean')
        
        summary_df = summary_df.sort_values('split_time')
        
        summary_df['smoothed'] = gaussian_filter1d(summary_df['mean'], 3)
        summary_df['derivative'] = summary_df['smoothed'].diff() / summary_df['split_time'].diff()
        summary_df['cumulative'] = summary_df['derivative'].cumsum()
        
        farray = np.array(summary_df['cumulative'])
        
        y_pos = summary_df.split_time.values
        
        ax[ax_index].errorbar(y_pos, farray, marker = 'o')

        ax[ax_index].xaxis.set_tick_params(rotation=90)
        ax[ax_index].set_title(f'{l}_split_{split}')
        ax[ax_index].set_ylabel('Cumulative growth')
        ax[ax_index].set_xlabel('Time point')
        ax_index += 1
        
plt.show()

sns.set(style="white", palette="Paired", color_codes=True)
fig, ax = plt.subplots(figsize=(7,5))
labels = []
lc = []
handles = []
all_lines = {}

total_df_no_first = total_df[total_df.n_split != '1'].copy()

cumulative_dict_dfs = {}

for l in total_df.line.unique():
    
    color = line_palette[l]

    sub = total_df[total_df.line == l]
    sub = sub.sort_values(by = 'datetime')
    sub = sub[sub.n_split != 'day']

    for split in sub.n_split.unique():


        subsub = sub[sub.n_split == split]

        if len(subsub.split_time.unique()) > 0:
    
            # user defined function,
            # with `area_sum` return the sum of the areas of all the field of view captured for that line at that time point
            summary_df = preprocess(subsub, original_v='Area (microm2)', final_output='mean')
            
            summary_df = summary_df.sort_values('split_time')
            
            summary_df['smoothed'] = gaussian_filter1d(summary_df['mean'], 3)
            summary_df['derivative'] = summary_df['smoothed'].diff() / summary_df['split_time'].diff()
            summary_df['cumulative'] = summary_df['derivative'].cumsum()
    
            cumulative_dict_dfs[f'{l}_{split}'] = summary_df
            
            farray = np.array(summary_df['cumulative'])
            
            y_pos = summary_df.split_time.values
    
            line, = ax.plot(y_pos, farray, color = color, marker = '.')
            ax.xaxis.set_tick_params(rotation=90)
            all_lines[f'{l}_{split}'] = line
    
            labels.append(l)
            handles.append(line)
            lc.append(color)
    
plt.legend(handles, labels, bbox_to_anchor = (1,1))

<matplotlib.legend.Legend at 0x7fe47fcdcb50>

lines = total_df.line.unique()

highlight_growth_curves(all_lines, 
                        xlabel = 'Hours from split', 
                        ylabel = 'Cumulative growth', 
                        lines = lines, fontsize = 20)
#plt.savefig('./figures/cumulative_growth_curve_per_line.svg', dpi = 300)

Fit linear model

I fit here a linear regression model taking into account all the cumulatve sums of all the splits for each line. We extrapolate the slope as the rate of growth of the line.

cumulative_df = pd.concat(cumulative_dict_dfs.values(), keys = cumulative_dict_dfs.keys()).reset_index()
cumulative_df['line'] = cumulative_df.level_0.apply(lambda x: x.split('_')[0])

cumulative_df

	level_0	level_1	time_point	mean	stds	hour	month	day	datetime	split_time	smoothed	derivative	cumulative	line
0	H1_1	0	06_11_23_t18	6.702764e+04	41616.484602	18	11	06	2023-11-06 18:00:00	0.0	151997.345803	NaN	NaN	H1
1	H1_1	2	07_11_23_t9	8.406022e+04	130798.841698	9	11	07	2023-11-07 09:00:00	15.0	189847.913490	2523.371179	2523.371179	H1
2	H1_1	1	07_11_23_t18	2.654972e+04	16684.343834	18	11	07	2023-11-07 18:00:00	24.0	269350.442789	8833.614367	11356.985546	H1
3	H1_1	4	08_11_23_t9	1.007394e+05	141517.200188	9	11	08	2023-11-08 09:00:00	39.0	396380.883270	8468.696032	19825.681578	H1
4	H1_1	3	08_11_23_t18	7.603012e+04	84318.866374	18	11	08	2023-11-08 18:00:00	48.0	576089.795294	19967.656892	39793.338469	H1
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
459	CTL01A_5	3	20_11_23_t9	2.595179e+05	88067.869959	9	11	20	2023-11-20 09:00:00	23.0	586571.010023	4211.355442	8525.392117	CTL01A
460	CTL01A_5	2	20_11_23_t18	8.738935e+05	625314.219906	18	11	20	2023-11-20 18:00:00	32.0	667181.708241	8956.744246	17482.136364	CTL01A
461	CTL01A_5	5	21_11_23_t9	7.845210e+05	489648.194587	9	11	21	2023-11-21 09:00:00	47.0	749884.816544	5513.540554	22995.676917	CTL01A
462	CTL01A_5	4	21_11_23_t17	5.332625e+05	NaN	17	11	21	2023-11-21 17:00:00	55.0	817761.601808	8484.598158	31480.275075	CTL01A
463	CTL01A_5	6	22_11_23_t10	1.589454e+06	NaN	10	11	22	2023-11-22 10:00:00	72.0	856047.818918	2252.130418	33732.405494	CTL01A

464 rows × 14 columns

# Initialize a grid of plots with an Axes for each walk
grid = sns.FacetGrid(cumulative_df.sort_values(by = 'split_time'), col="line", palette=line_palette,
                     col_wrap=4, height=5)

grid.map(sns.regplot, "split_time", "cumulative", order = 1)

# Adjust the arrangement of the plots
grid.fig.tight_layout(w_pad=1)

fitted_model = {}
for l in cumulative_df.line.unique():
    
    sub = cumulative_df[cumulative_df.line == l]
    sub = sub.sort_values(by = 'datetime')

    key = f'{l}'
    fitted_model[key] = {}
    fitted_model[key]['slope'], fitted_model[key]['intercept'], fitted_model[key]['rvalue'], fitted_model[key]['pvalue'], fitted_model[key]['stderr'] = stats.linregress(sub['split_time'], sub['cumulative'].fillna(0))

fitted_model_df = pd.DataFrame.from_dict(fitted_model).T.reset_index()
fitted_model_df['line'] = fitted_model_df['index'].apply(lambda x: x.split('_')[0])
fitted_model_df.sort_values(by = 'slope')

	index	slope	intercept	rvalue	pvalue	stderr	line
11	CTL01A	889.158749	-3317.415096	0.658753	3.427561e-04	211.747106	CTL01A
0	H1	1507.258668	-24661.605065	0.929554	3.246271e-13	115.050563	H1
1	CTL04E	2701.742613	-29608.142008	0.849852	4.029196e-12	271.791859	CTL04E
3	CTL05A	2763.552397	-34043.044124	0.858594	5.454580e-12	275.014498	CTL05A
5	KTD8.2	2930.111544	-64281.188697	0.961890	3.878081e-24	131.700799	KTD8.2
10	UCSFi001-A	3326.563394	-48138.442881	0.873562	1.020601e-14	285.989085	UCSFi001-A
4	H9	5258.813593	-86560.673508	0.940884	5.551798e-19	311.244699	H9
9	CTL07C	5615.863178	-135367.457446	0.872476	2.224665e-13	510.241618	CTL07C
8	CTL08A	5884.302391	-142089.468408	0.888082	9.120149e-16	469.977991	CTL08A
7	CTL06F	6314.448619	-150942.297102	0.905129	3.365469e-17	457.644407	CTL06F
6	CTL09A	6938.961586	-121941.446019	0.895983	1.307039e-14	565.410212	CTL09A
2	CTL02A	7219.721473	-126601.267281	0.858920	1.340509e-12	698.296028	CTL02A

fitted_model_df.rvalue.mean()

0.8744732639082721

fitted_model_df.sort_values(by = 'slope').to_csv('../../data/csv/iPSC_fitted_lm_grouped.csv')